TSTP Solution File: LCL504+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL504+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 06:54:25 EDT 2023
% Result : Theorem 5.91s 6.11s
% Output : CNFRefutation 5.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 110
% Syntax : Number of formulae : 324 ( 98 unt; 92 typ; 0 def)
% Number of atoms : 432 ( 52 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 379 ( 179 ~; 179 |; 10 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 34 ( 32 usr; 32 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 55 con; 0-2 aty)
% Number of variables : 446 ( 89 sgn; 36 !; 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,
esk1_0: $i ).
tff(decl_60,type,
esk2_0: $i ).
tff(decl_61,type,
esk3_0: $i ).
tff(decl_62,type,
esk4_0: $i ).
tff(decl_63,type,
esk5_0: $i ).
tff(decl_64,type,
esk6_0: $i ).
tff(decl_65,type,
esk7_0: $i ).
tff(decl_66,type,
esk8_0: $i ).
tff(decl_67,type,
esk9_0: $i ).
tff(decl_68,type,
esk10_0: $i ).
tff(decl_69,type,
esk11_0: $i ).
tff(decl_70,type,
esk12_0: $i ).
tff(decl_71,type,
esk13_0: $i ).
tff(decl_72,type,
esk14_0: $i ).
tff(decl_73,type,
esk15_0: $i ).
tff(decl_74,type,
esk16_0: $i ).
tff(decl_75,type,
esk17_0: $i ).
tff(decl_76,type,
esk18_0: $i ).
tff(decl_77,type,
esk19_0: $i ).
tff(decl_78,type,
esk20_0: $i ).
tff(decl_79,type,
esk21_0: $i ).
tff(decl_80,type,
esk22_0: $i ).
tff(decl_81,type,
esk23_0: $i ).
tff(decl_82,type,
esk24_0: $i ).
tff(decl_83,type,
esk25_0: $i ).
tff(decl_84,type,
esk26_0: $i ).
tff(decl_85,type,
esk27_0: $i ).
tff(decl_86,type,
esk28_0: $i ).
tff(decl_87,type,
esk29_0: $i ).
tff(decl_88,type,
esk30_0: $i ).
tff(decl_89,type,
esk31_0: $i ).
tff(decl_90,type,
esk32_0: $i ).
tff(decl_91,type,
esk33_0: $i ).
tff(decl_92,type,
esk34_0: $i ).
tff(decl_93,type,
esk35_0: $i ).
tff(decl_94,type,
esk36_0: $i ).
tff(decl_95,type,
esk37_0: $i ).
tff(decl_96,type,
esk38_0: $i ).
tff(decl_97,type,
esk39_0: $i ).
tff(decl_98,type,
esk40_0: $i ).
tff(decl_99,type,
esk41_0: $i ).
tff(decl_100,type,
esk42_0: $i ).
tff(decl_101,type,
esk43_0: $i ).
tff(decl_102,type,
esk44_0: $i ).
tff(decl_103,type,
esk45_0: $i ).
tff(decl_104,type,
esk46_0: $i ).
tff(decl_105,type,
esk47_0: $i ).
tff(decl_106,type,
esk48_0: $i ).
tff(decl_107,type,
esk49_0: $i ).
tff(decl_108,type,
esk50_0: $i ).
tff(decl_109,type,
esk51_0: $i ).
tff(decl_110,type,
esk52_0: $i ).
tff(decl_111,type,
esk53_0: $i ).
tff(decl_112,type,
esk54_0: $i ).
tff(decl_113,type,
esk55_0: $i ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(kn3,axiom,
( kn3
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(not(and(X5,X6)),not(and(X6,X4))))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(rosser_kn3,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(rosser_kn2,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(rosser_kn1,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(rosser_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_equiv) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',substitution_of_equivalents) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(hilbert_implies_2,conjecture,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(c_0_18,plain,
! [X121,X122] :
( ~ op_implies_and
| implies(X121,X122) = not(and(X121,not(X122))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).
fof(c_0_19,plain,
! [X117,X118] :
( ~ op_or
| or(X117,X118) = not(and(not(X117),not(X118))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])]) ).
cnf(c_0_20,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
fof(c_0_22,plain,
! [X7,X8] :
( ( ~ modus_ponens
| ~ is_a_theorem(X7)
| ~ is_a_theorem(implies(X7,X8))
| is_a_theorem(X8) )
& ( is_a_theorem(esk1_0)
| modus_ponens )
& ( is_a_theorem(implies(esk1_0,esk2_0))
| modus_ponens )
& ( ~ is_a_theorem(esk2_0)
| modus_ponens ) ),
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])])])])]) ).
fof(c_0_23,plain,
! [X77,X78,X79] :
( ( ~ kn3
| is_a_theorem(implies(implies(X77,X78),implies(not(and(X78,X79)),not(and(X79,X77))))) )
& ( ~ is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0)))))
| kn3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])]) ).
cnf(c_0_24,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_26,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
cnf(c_0_27,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).
cnf(c_0_29,plain,
( is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1)))))
| ~ kn3 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
kn3,
inference(split_conjunct,[status(thm)],[rosser_kn3]) ).
cnf(c_0_32,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_34,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X2,X1))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_35,plain,
( is_a_theorem(or(and(X1,X2),not(and(X2,X3))))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_36,plain,
! [X73,X74] :
( ( ~ kn2
| is_a_theorem(implies(and(X73,X74),X73)) )
& ( ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))
| kn2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])]) ).
cnf(c_0_37,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(and(X3,X1)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ kn2 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_39,plain,
kn2,
inference(split_conjunct,[status(thm)],[rosser_kn2]) ).
fof(c_0_40,plain,
! [X71] :
( ( ~ kn1
| is_a_theorem(implies(X71,and(X71,X71))) )
& ( ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))
| kn1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])]) ).
cnf(c_0_41,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_37,c_0_25]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_43,plain,
( is_a_theorem(implies(X1,and(X1,X1)))
| ~ kn1 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_44,plain,
kn1,
inference(split_conjunct,[status(thm)],[rosser_kn1]) ).
cnf(c_0_45,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(implies(X2,and(X1,X3))) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_47,plain,
( is_a_theorem(or(and(X1,X2),implies(X2,X3)))
| ~ is_a_theorem(or(X3,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_25]),c_0_30]) ).
cnf(c_0_48,plain,
is_a_theorem(not(and(not(X1),X1))),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(and(X3,X1)))
| ~ is_a_theorem(or(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_47]) ).
cnf(c_0_50,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,and(X1,X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_30]),c_0_25]),c_0_30]) ).
cnf(c_0_51,plain,
is_a_theorem(or(not(X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_25]),c_0_30]) ).
cnf(c_0_52,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(or(X2,X3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_25]),c_0_30]) ).
cnf(c_0_53,plain,
is_a_theorem(or(X1,not(and(X1,X2)))),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
( is_a_theorem(or(and(X1,X1),X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_55,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_25,c_0_25]) ).
cnf(c_0_56,plain,
is_a_theorem(or(X1,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_53,c_0_25]) ).
cnf(c_0_57,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(and(X2,X2)))
| ~ is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_54]) ).
cnf(c_0_58,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_53]) ).
cnf(c_0_59,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_37,c_0_48]) ).
cnf(c_0_60,plain,
implies(X1,and(not(X2),not(X3))) = not(and(X1,or(X2,X3))),
inference(spm,[status(thm)],[c_0_55,c_0_30]) ).
cnf(c_0_61,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_56]) ).
cnf(c_0_62,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,plain,
is_a_theorem(or(X1,and(not(X1),not(X1)))),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
cnf(c_0_64,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_25]),c_0_30]) ).
cnf(c_0_65,plain,
is_a_theorem(not(and(not(X1),or(X1,X1)))),
inference(spm,[status(thm)],[c_0_46,c_0_60]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(and(not(X1),X1),X2)),
inference(spm,[status(thm)],[c_0_61,c_0_48]) ).
cnf(c_0_67,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_25]),c_0_30]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_64,c_0_51]) ).
cnf(c_0_69,plain,
( is_a_theorem(implies(or(X1,X1),X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_49,c_0_65]) ).
cnf(c_0_70,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,and(not(X3),X3))) ),
inference(spm,[status(thm)],[c_0_52,c_0_66]) ).
cnf(c_0_71,plain,
( is_a_theorem(implies(and(X1,X2),and(X3,X1)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_64,c_0_35]) ).
cnf(c_0_72,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(or(and(X1,X1),X1)) ),
inference(spm,[status(thm)],[c_0_67,c_0_54]) ).
cnf(c_0_73,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_68]) ).
cnf(c_0_74,plain,
is_a_theorem(implies(or(X1,X1),not(not(X1)))),
inference(spm,[status(thm)],[c_0_69,c_0_51]) ).
cnf(c_0_75,plain,
is_a_theorem(or(X1,not(and(not(X2),X2)))),
inference(spm,[status(thm)],[c_0_70,c_0_51]) ).
cnf(c_0_76,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(X2,X3))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_71]) ).
cnf(c_0_77,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_72,c_0_54]) ).
cnf(c_0_78,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_73]),c_0_30]) ).
cnf(c_0_79,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(or(X1,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_74]) ).
cnf(c_0_80,plain,
is_a_theorem(or(X1,or(not(X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_25]),c_0_30]) ).
fof(c_0_81,plain,
! [X125,X126] :
( ~ op_equiv
| equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])]) ).
cnf(c_0_82,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(or(X2,X2)) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_78]) ).
cnf(c_0_84,plain,
is_a_theorem(not(not(or(not(X1),X1)))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_86,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).
fof(c_0_87,plain,
! [X11,X12] :
( ( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X11,X12))
| X11 = X12 )
& ( is_a_theorem(equiv(esk3_0,esk4_0))
| substitution_of_equivalents )
& ( esk3_0 != esk4_0
| substitution_of_equivalents ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])]) ).
cnf(c_0_88,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(or(X2,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_89,plain,
is_a_theorem(or(or(not(X1),X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_84]),c_0_30]) ).
cnf(c_0_90,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]) ).
cnf(c_0_91,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_92,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_93,plain,
( is_a_theorem(and(X1,or(not(X2),X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_94,plain,
and(implies(X1,not(X2)),or(X2,X1)) = equiv(X1,not(X2)),
inference(spm,[status(thm)],[c_0_90,c_0_30]) ).
cnf(c_0_95,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,not(X3)))
| ~ is_a_theorem(or(X3,X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_30]) ).
cnf(c_0_96,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).
cnf(c_0_97,plain,
is_a_theorem(equiv(X1,not(not(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_68])]) ).
cnf(c_0_98,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(and(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_95,c_0_53]) ).
cnf(c_0_99,plain,
not(not(X1)) = X1,
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_100,plain,
is_a_theorem(or(implies(and(X1,X2),X3),X1)),
inference(spm,[status(thm)],[c_0_98,c_0_56]) ).
cnf(c_0_101,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_25,c_0_99]) ).
cnf(c_0_102,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(implies(and(X1,X2),X3))) ),
inference(spm,[status(thm)],[c_0_34,c_0_100]) ).
cnf(c_0_103,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_99,c_0_101]) ).
cnf(c_0_104,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_46]) ).
cnf(c_0_105,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(and(and(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_106,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_104]) ).
cnf(c_0_107,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,and(X1,X3)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_108,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(and(X2,X3))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_107,c_0_71]) ).
cnf(c_0_109,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(or(X2,X2)) ),
inference(spm,[status(thm)],[c_0_108,c_0_77]) ).
cnf(c_0_110,plain,
or(not(X1),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_99]) ).
cnf(c_0_111,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,not(X2)))
| ~ is_a_theorem(or(X2,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_30]),c_0_110]) ).
cnf(c_0_112,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(and(not(X2),X2),X1)) ),
inference(spm,[status(thm)],[c_0_111,c_0_66]) ).
cnf(c_0_113,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_114,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(not(X3)) ),
inference(spm,[status(thm)],[c_0_37,c_0_58]) ).
cnf(c_0_115,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_99]),c_0_113]) ).
cnf(c_0_116,plain,
is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_30]) ).
cnf(c_0_117,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(and(X2,X2))) ),
inference(spm,[status(thm)],[c_0_114,c_0_46]) ).
cnf(c_0_118,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(and(not(X3),X3),X1)) ),
inference(spm,[status(thm)],[c_0_95,c_0_75]) ).
cnf(c_0_119,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(or(X2,not(X2)),X1)) ),
inference(spm,[status(thm)],[c_0_115,c_0_30]) ).
cnf(c_0_120,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_30]),c_0_113]) ).
cnf(c_0_121,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(and(X1,X3)) ),
inference(spm,[status(thm)],[c_0_45,c_0_83]) ).
cnf(c_0_122,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_25]),c_0_25]),c_0_30]) ).
cnf(c_0_123,plain,
and(X1,not(X2)) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_103,c_0_99]) ).
cnf(c_0_124,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(implies(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_98,c_0_113]) ).
cnf(c_0_125,plain,
( is_a_theorem(or(implies(X1,X2),X3))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_118,c_0_47]) ).
cnf(c_0_126,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_62,c_0_110]) ).
cnf(c_0_127,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_30]) ).
cnf(c_0_128,plain,
( is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_104]) ).
cnf(c_0_129,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,not(X3)))
| ~ is_a_theorem(or(X2,X3)) ),
inference(spm,[status(thm)],[c_0_49,c_0_59]) ).
cnf(c_0_130,plain,
is_a_theorem(implies(X1,not(and(not(X2),X2)))),
inference(spm,[status(thm)],[c_0_122,c_0_75]) ).
cnf(c_0_131,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_78]) ).
cnf(c_0_132,plain,
is_a_theorem(or(X1,not(or(X1,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_123]),c_0_30]) ).
cnf(c_0_133,plain,
is_a_theorem(or(not(not(implies(X1,X2))),X1)),
inference(spm,[status(thm)],[c_0_124,c_0_68]) ).
cnf(c_0_134,plain,
is_a_theorem(or(implies(X1,not(not(X1))),X2)),
inference(spm,[status(thm)],[c_0_125,c_0_51]) ).
cnf(c_0_135,plain,
( is_a_theorem(not(or(X1,X2)))
| ~ is_a_theorem(not(or(X2,X1))) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_136,plain,
not(or(X1,not(X2))) = and(not(X1),X2),
inference(spm,[status(thm)],[c_0_103,c_0_30]) ).
cnf(c_0_137,plain,
( is_a_theorem(not(and(not(not(not(X1))),X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_41,c_0_68]) ).
cnf(c_0_138,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,not(X3)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_128]) ).
cnf(c_0_139,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,and(not(X3),X3))) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_140,plain,
( is_a_theorem(or(implies(X1,X2),X3))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_78]) ).
cnf(c_0_141,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X3,X1))
| ~ is_a_theorem(not(X3)) ),
inference(spm,[status(thm)],[c_0_95,c_0_131]) ).
cnf(c_0_142,plain,
is_a_theorem(or(not(X1),or(X1,X2))),
inference(spm,[status(thm)],[c_0_56,c_0_30]) ).
cnf(c_0_143,plain,
and(or(X1,X2),implies(X2,not(X1))) = equiv(not(X1),X2),
inference(spm,[status(thm)],[c_0_90,c_0_30]) ).
cnf(c_0_144,plain,
( is_a_theorem(not(and(not(and(X1,X1)),X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_41,c_0_46]) ).
cnf(c_0_145,plain,
is_a_theorem(or(implies(or(X1,X1),X1),X2)),
inference(spm,[status(thm)],[c_0_125,c_0_132]) ).
cnf(c_0_146,plain,
is_a_theorem(implies(X1,not(not(or(X1,X2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_133]),c_0_30]) ).
cnf(c_0_147,plain,
is_a_theorem(not(not(implies(X1,not(not(X1)))))),
inference(spm,[status(thm)],[c_0_79,c_0_134]) ).
cnf(c_0_148,plain,
( is_a_theorem(not(implies(X1,X2)))
| ~ is_a_theorem(and(not(X2),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_110]) ).
cnf(c_0_149,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(or(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_95,c_0_132]) ).
cnf(c_0_150,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_101]),c_0_99]),c_0_30]) ).
cnf(c_0_151,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X3)))
| ~ is_a_theorem(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_30]),c_0_25]) ).
cnf(c_0_152,plain,
( is_a_theorem(equiv(X1,X2))
| ~ is_a_theorem(implies(implies(X2,X1),implies(X1,X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_106,c_0_90]) ).
cnf(c_0_153,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_154,plain,
( is_a_theorem(or(or(X1,X2),X3))
| ~ is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_155,plain,
( is_a_theorem(not(equiv(not(X1),X2)))
| ~ is_a_theorem(implies(implies(X2,not(X1)),not(or(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_59,c_0_143]) ).
cnf(c_0_156,plain,
( is_a_theorem(implies(implies(X1,not(X1)),not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_101]),c_0_101]) ).
cnf(c_0_157,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(spm,[status(thm)],[c_0_74,c_0_99]) ).
cnf(c_0_158,plain,
implies(or(X1,X2),and(X2,not(not(X1)))) = not(equiv(not(X1),X2)),
inference(spm,[status(thm)],[c_0_55,c_0_143]) ).
cnf(c_0_159,plain,
is_a_theorem(implies(X1,implies(or(X2,X2),X2))),
inference(spm,[status(thm)],[c_0_139,c_0_145]) ).
cnf(c_0_160,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(spm,[status(thm)],[c_0_146,c_0_99]) ).
cnf(c_0_161,plain,
is_a_theorem(implies(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_99]),c_0_99]) ).
cnf(c_0_162,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(X2,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_99]),c_0_103]) ).
cnf(c_0_163,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,or(X2,X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_110]) ).
cnf(c_0_164,plain,
( is_a_theorem(implies(implies(X1,X2),or(X2,X3)))
| ~ is_a_theorem(or(X3,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_30]),c_0_113]) ).
cnf(c_0_165,plain,
( is_a_theorem(implies(X1,not(not(X2))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_151,c_0_51]) ).
cnf(c_0_166,plain,
( is_a_theorem(equiv(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_167,plain,
( is_a_theorem(or(or(X1,X2),X3))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_154,c_0_73]) ).
cnf(c_0_168,plain,
is_a_theorem(or(X1,not(not(not(X1))))),
inference(spm,[status(thm)],[c_0_68,c_0_30]) ).
cnf(c_0_169,plain,
is_a_theorem(not(equiv(not(X1),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157])]) ).
cnf(c_0_170,plain,
implies(or(X1,X2),and(X2,X1)) = not(equiv(not(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_123]),c_0_103]) ).
cnf(c_0_171,plain,
is_a_theorem(equiv(or(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_159]),c_0_160])]) ).
cnf(c_0_172,plain,
is_a_theorem(or(implies(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_124,c_0_161]) ).
cnf(c_0_173,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_162,c_0_106]) ).
cnf(c_0_174,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_175,plain,
( is_a_theorem(or(X1,not(not(X2))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_165,c_0_30]) ).
cnf(c_0_176,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_96,c_0_166]) ).
cnf(c_0_177,plain,
( is_a_theorem(implies(X1,or(X2,X3)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_139,c_0_167]) ).
cnf(c_0_178,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(not(not(X2)),X1)) ),
inference(spm,[status(thm)],[c_0_95,c_0_168]) ).
cnf(c_0_179,plain,
is_a_theorem(implies(X1,or(not(X2),X2))),
inference(spm,[status(thm)],[c_0_122,c_0_80]) ).
cnf(c_0_180,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(implies(or(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_124,c_0_30]) ).
cnf(c_0_181,plain,
is_a_theorem(implies(or(X1,X1),and(X1,X1))),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_182,plain,
or(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_96,c_0_171]) ).
cnf(c_0_183,plain,
is_a_theorem(implies(or(X1,X1),or(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_172]),c_0_30]) ).
cnf(c_0_184,plain,
and(or(X1,not(X2)),or(X2,not(X1))) = equiv(not(X1),not(X2)),
inference(spm,[status(thm)],[c_0_94,c_0_30]) ).
cnf(c_0_185,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_108,c_0_173]) ).
cnf(c_0_186,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_30]),c_0_110]) ).
cnf(c_0_187,plain,
( or(X1,X2) = X3
| ~ is_a_theorem(X3)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_176,c_0_177]) ).
cnf(c_0_188,plain,
is_a_theorem(or(or(not(X1),X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_56]),c_0_30]) ).
cnf(c_0_189,plain,
( implies(X1,X1) = X2
| ~ is_a_theorem(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_179]),c_0_110]) ).
cnf(c_0_190,plain,
is_a_theorem(or(and(X1,X1),not(X1))),
inference(spm,[status(thm)],[c_0_180,c_0_181]) ).
cnf(c_0_191,plain,
and(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_182]),c_0_99]),c_0_99]) ).
cnf(c_0_192,plain,
( or(X1,X2) = X1
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_183]),c_0_182]),c_0_182]) ).
cnf(c_0_193,plain,
equiv(not(X1),X1) = not(implies(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_182]),c_0_99]),c_0_182]),c_0_123]),c_0_99]) ).
cnf(c_0_194,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,or(X1,X1)))
| ~ is_a_theorem(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_74]),c_0_99]) ).
cnf(c_0_195,plain,
( implies(X1,X2) = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_176,c_0_186]) ).
cnf(c_0_196,plain,
( or(X1,X2) = or(implies(X3,X4),X3)
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_110]) ).
cnf(c_0_197,plain,
is_a_theorem(or(or(X1,not(X1)),X2)),
inference(spm,[status(thm)],[c_0_89,c_0_99]) ).
cnf(c_0_198,plain,
implies(X1,X1) = or(X2,not(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_191]) ).
cnf(c_0_199,plain,
or(implies(X1,X1),X2) = implies(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_169]),c_0_110]),c_0_193]),c_0_30]),c_0_193]),c_0_99]) ).
cnf(c_0_200,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_194,c_0_164]) ).
cnf(c_0_201,plain,
is_a_theorem(or(or(X1,X2),not(X2))),
inference(spm,[status(thm)],[c_0_180,c_0_127]) ).
cnf(c_0_202,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(or(X1,X3)))) ),
inference(spm,[status(thm)],[c_0_129,c_0_146]) ).
cnf(c_0_203,plain,
( or(X1,X2) = X2
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_195,c_0_30]) ).
cnf(c_0_204,plain,
or(implies(X1,X2),X1) = implies(esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_198]),c_0_199]),c_0_199]) ).
cnf(c_0_205,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X2,X1))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_150]),c_0_30]) ).
cnf(c_0_206,plain,
is_a_theorem(or(implies(X1,or(X2,X1)),X3)),
inference(spm,[status(thm)],[c_0_125,c_0_201]) ).
cnf(c_0_207,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(or(X1,X3),X2)) ),
inference(spm,[status(thm)],[c_0_202,c_0_150]) ).
cnf(c_0_208,plain,
( implies(esk1_0,esk1_0) = X1
| ~ is_a_theorem(not(implies(X1,X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_161])]) ).
cnf(c_0_209,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,or(X3,X2)),X1)) ),
inference(spm,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_210,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(spm,[status(thm)],[c_0_207,c_0_127]) ).
cnf(c_0_211,plain,
( implies(esk1_0,esk1_0) = X1
| ~ is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_208,c_0_103]) ).
cnf(c_0_212,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,implies(X3,X2)),X1)) ),
inference(spm,[status(thm)],[c_0_209,c_0_110]) ).
cnf(c_0_213,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_210,c_0_110]) ).
cnf(c_0_214,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_78]) ).
cnf(c_0_215,plain,
( implies(esk1_0,esk1_0) = X1
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_211,c_0_106]) ).
cnf(c_0_216,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_212,c_0_213]) ).
cnf(c_0_217,plain,
is_a_theorem(implies(implies(or(X1,X2),X3),or(and(X3,implies(X2,not(X1))),not(equiv(X2,not(X1)))))),
inference(spm,[status(thm)],[c_0_33,c_0_94]) ).
cnf(c_0_218,plain,
( is_a_theorem(equiv(X1,X2))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_214,c_0_90]) ).
cnf(c_0_219,plain,
( implies(X1,implies(X2,X1)) = implies(esk1_0,esk1_0)
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_215,c_0_216]) ).
cnf(c_0_220,plain,
is_a_theorem(or(or(and(X1,implies(X2,not(X3))),not(equiv(X2,not(X3)))),or(X3,X2))),
inference(spm,[status(thm)],[c_0_124,c_0_217]) ).
fof(c_0_221,plain,
! [X23,X24] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X23,implies(X23,X24)),implies(X23,X24))) )
& ( ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0)))
| implies_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])]) ).
fof(c_0_222,negated_conjecture,
~ implies_2,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_implies_2])]) ).
cnf(c_0_223,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_96,c_0_218]) ).
cnf(c_0_224,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),X1)),
inference(spm,[status(thm)],[c_0_174,c_0_56]) ).
cnf(c_0_225,plain,
implies(X1,implies(X2,X1)) = implies(esk1_0,esk1_0),
inference(spm,[status(thm)],[c_0_219,c_0_220]) ).
cnf(c_0_226,plain,
( implies_2
| ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))) ),
inference(split_conjunct,[status(thm)],[c_0_221]) ).
cnf(c_0_227,negated_conjecture,
~ implies_2,
inference(split_conjunct,[status(thm)],[c_0_222]) ).
cnf(c_0_228,plain,
implies(implies(X1,X2),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_225]),c_0_161])]) ).
cnf(c_0_229,plain,
~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))),
inference(sr,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_230,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_228,c_0_228]) ).
cnf(c_0_231,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_230]),c_0_161])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL504+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 04:53:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.58 start to proof: theBenchmark
% 5.91/6.11 % Version : CSE_E---1.5
% 5.91/6.11 % Problem : theBenchmark.p
% 5.91/6.11 % Proof found
% 5.91/6.11 % SZS status Theorem for theBenchmark.p
% 5.91/6.11 % SZS output start Proof
% See solution above
% 5.91/6.13 % Total time : 5.519000 s
% 5.91/6.13 % SZS output end Proof
% 5.91/6.13 % Total time : 5.523000 s
%------------------------------------------------------------------------------