TSTP Solution File: LCL499+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL499+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 : n014.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 06:54:24 EDT 2023
% Result : Theorem 0.21s 0.57s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 104
% Syntax : Number of formulae : 134 ( 20 unt; 92 typ; 0 def)
% Number of atoms : 83 ( 8 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 69 ( 28 ~; 27 |; 7 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 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 : 45 ( 0 sgn; 20 !; 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(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(r3,axiom,
( r3
<=> ! [X4,X5] : is_a_theorem(implies(or(X4,X5),or(X5,X4))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(principia_r3,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(r1,axiom,
( r1
<=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(op_and,axiom,
( op_and
=> ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(rosser_kn1,conjecture,
kn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn1) ).
fof(principia_r1,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
fof(c_0_12,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_13,plain,
! [X101,X102] :
( ( ~ r3
| is_a_theorem(implies(or(X101,X102),or(X102,X101))) )
& ( ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))
| r3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])]) ).
cnf(c_0_14,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).
cnf(c_0_16,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
| ~ r3 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]) ).
fof(c_0_18,plain,
! [X123,X124] :
( ~ op_implies_or
| implies(X123,X124) = or(not(X123),X124) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])]) ).
cnf(c_0_19,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_14,c_0_15])]) ).
cnf(c_0_20,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_21,plain,
( implies(X1,X2) = or(not(X1),X2)
| ~ op_implies_or ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
cnf(c_0_23,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
fof(c_0_25,plain,
! [X95] :
( ( ~ r1
| is_a_theorem(implies(or(X95,X95),X95)) )
& ( ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))
| r1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])]) ).
fof(c_0_26,plain,
! [X119,X120] :
( ~ op_and
| and(X119,X120) = not(or(not(X119),not(X120))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])]) ).
fof(c_0_27,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])])])]) ).
fof(c_0_28,negated_conjecture,
~ kn1,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[rosser_kn1])]) ).
cnf(c_0_29,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( is_a_theorem(implies(or(X1,X1),X1))
| ~ r1 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
r1,
inference(split_conjunct,[status(thm)],[principia_r1]) ).
cnf(c_0_32,plain,
( and(X1,X2) = not(or(not(X1),not(X2)))
| ~ op_and ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
cnf(c_0_34,plain,
( kn1
| ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
~ kn1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
cnf(c_0_38,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_24]),c_0_33])]) ).
cnf(c_0_39,plain,
~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0))),
inference(sr,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_24]),c_0_38]) ).
cnf(c_0_41,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL499+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 18:29:34 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.54 start to proof: theBenchmark
% 0.21/0.57 % Version : CSE_E---1.5
% 0.21/0.57 % Problem : theBenchmark.p
% 0.21/0.57 % Proof found
% 0.21/0.57 % SZS status Theorem for theBenchmark.p
% 0.21/0.57 % SZS output start Proof
% See solution above
% 0.21/0.57 % Total time : 0.020000 s
% 0.21/0.57 % SZS output end Proof
% 0.21/0.57 % Total time : 0.024000 s
%------------------------------------------------------------------------------