TSTP Solution File: LCL497+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL497+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n025.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 : Tue Aug 22 10:48:14 EDT 2023
% Result : Theorem 113.66s 83.49s
% Output : CNFRefutation 113.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 114
% Syntax : Number of formulae : 194 ( 51 unt; 93 typ; 0 def)
% Number of atoms : 160 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 109 ( 50 ~; 46 |; 1 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 35 ( 33 usr; 33 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 55 con; 0-2 aty)
% Number of variables : 163 (; 163 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > or > implies > equiv > and > #nlpp > not > substitution_of_equivalents > r5 > r4 > r3 > r2 > r1 > or_3 > or_2 > or_1 > op_or > op_implies_or > op_implies_and > op_implies > op_equiv > op_and > modus_tollens > modus_ponens > kn3 > kn2 > kn1 > implies_3 > implies_2 > implies_1 > equivalence_3 > equivalence_2 > equivalence_1 > cn3 > cn2 > cn1 > and_3 > and_2 > and_1 > #skF_33 > #skF_41 > #skF_52 > #skF_49 > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_31 > #skF_15 > #skF_25 > #skF_55 > #skF_38 > #skF_36 > #skF_54 > #skF_43 > #skF_19 > #skF_40 > #skF_48 > #skF_7 > #skF_37 > #skF_10 > #skF_16 > #skF_47 > #skF_26 > #skF_53 > #skF_14 > #skF_51 > #skF_5 > #skF_45 > #skF_46 > #skF_39 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_1 > #skF_21 > #skF_9 > #skF_32 > #skF_50 > #skF_8 > #skF_30 > #skF_42 > #skF_4 > #skF_22 > #skF_29 > #skF_28 > #skF_35 > #skF_24 > #skF_27 > #skF_23 > #skF_44 > #skF_12 > #skF_34
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(implies_2,type,
implies_2: $o ).
tff(r1,type,
r1: $o ).
tff(equiv,type,
equiv: ( $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': $i ).
tff('#skF_41',type,
'#skF_41': $i ).
tff(r3,type,
r3: $o ).
tff('#skF_52',type,
'#skF_52': $i ).
tff(equivalence_2,type,
equivalence_2: $o ).
tff('#skF_49',type,
'#skF_49': $i ).
tff(and_2,type,
and_2: $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff(op_implies_or,type,
op_implies_or: $o ).
tff('#skF_18',type,
'#skF_18': $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff(r5,type,
r5: $o ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(kn3,type,
kn3: $o ).
tff('#skF_31',type,
'#skF_31': $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff('#skF_25',type,
'#skF_25': $i ).
tff(cn2,type,
cn2: $o ).
tff('#skF_55',type,
'#skF_55': $i ).
tff(r4,type,
r4: $o ).
tff('#skF_38',type,
'#skF_38': $i ).
tff('#skF_36',type,
'#skF_36': $i ).
tff('#skF_54',type,
'#skF_54': $i ).
tff('#skF_43',type,
'#skF_43': $i ).
tff(op_and,type,
op_and: $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff('#skF_40',type,
'#skF_40': $i ).
tff('#skF_48',type,
'#skF_48': $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_37',type,
'#skF_37': $i ).
tff(and_3,type,
and_3: $o ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(op_implies_and,type,
op_implies_and: $o ).
tff(equivalence_1,type,
equivalence_1: $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(kn2,type,
kn2: $o ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(equivalence_3,type,
equivalence_3: $o ).
tff(and_1,type,
and_1: $o ).
tff('#skF_47',type,
'#skF_47': $i ).
tff(cn1,type,
cn1: $o ).
tff('#skF_26',type,
'#skF_26': $i ).
tff('#skF_53',type,
'#skF_53': $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_51',type,
'#skF_51': $i ).
tff(or_1,type,
or_1: $o ).
tff(implies_3,type,
implies_3: $o ).
tff('#skF_5',type,
'#skF_5': $i ).
tff('#skF_45',type,
'#skF_45': $i ).
tff('#skF_46',type,
'#skF_46': $i ).
tff('#skF_39',type,
'#skF_39': $i ).
tff(or,type,
or: ( $i * $i ) > $i ).
tff(modus_tollens,type,
modus_tollens: $o ).
tff(r2,type,
r2: $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(not,type,
not: $i > $i ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(modus_ponens,type,
modus_ponens: $o ).
tff(op_or,type,
op_or: $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(substitution_of_equivalents,type,
substitution_of_equivalents: $o ).
tff('#skF_1',type,
'#skF_1': $i ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_32',type,
'#skF_32': $i ).
tff(op_equiv,type,
op_equiv: $o ).
tff('#skF_50',type,
'#skF_50': $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_30',type,
'#skF_30': $i ).
tff('#skF_42',type,
'#skF_42': $i ).
tff(or_3,type,
or_3: $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_22',type,
'#skF_22': $i ).
tff(kn1,type,
kn1: $o ).
tff('#skF_29',type,
'#skF_29': $i ).
tff('#skF_28',type,
'#skF_28': $i ).
tff('#skF_35',type,
'#skF_35': $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff('#skF_27',type,
'#skF_27': $i ).
tff('#skF_23',type,
'#skF_23': $i ).
tff(and,type,
and: ( $i * $i ) > $i ).
tff(implies_1,type,
implies_1: $o ).
tff('#skF_44',type,
'#skF_44': $i ).
tff(op_implies,type,
op_implies: $o ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(cn3,type,
cn3: $o ).
tff(or_2,type,
or_2: $o ).
tff('#skF_12',type,
'#skF_12': $i ).
tff('#skF_34',type,
'#skF_34': $i ).
tff(f_243,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
tff(f_210,axiom,
( op_implies_or
=> ! [X,Y] : ( implies(X,Y) = or(not(X),Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
tff(f_251,axiom,
r3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
tff(f_159,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r3) ).
tff(f_250,axiom,
r2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
tff(f_155,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r2) ).
tff(f_254,axiom,
r5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
tff(f_168,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r5) ).
tff(f_247,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
tff(f_60,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_100,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_1) ).
tff(f_261,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_or) ).
tff(f_198,axiom,
( op_or
=> ! [X,Y] : ( or(X,Y) = not(and(not(X),not(Y))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
tff(f_253,axiom,
r4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
tff(f_164,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r4) ).
tff(f_249,axiom,
r1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
tff(f_151,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
tff(f_244,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
tff(f_202,axiom,
( op_and
=> ! [X,Y] : ( and(X,Y) = not(or(not(X),not(Y))) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_and) ).
tff(f_265,negated_conjecture,
~ cn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn2) ).
tff(f_142,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn2) ).
tff(c_122,plain,
op_implies_or,
inference(cnfTransformation,[status(thm)],[f_243]) ).
tff(c_118,plain,
! [X_62,Y_63] :
( ( or(not(X_62),Y_63) = implies(X_62,Y_63) )
| ~ op_implies_or ),
inference(cnfTransformation,[status(thm)],[f_210]) ).
tff(c_153,plain,
! [X_62,Y_63] : ( or(not(X_62),Y_63) = implies(X_62,Y_63) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_134,plain,
r3,
inference(cnfTransformation,[status(thm)],[f_251]) ).
tff(c_102,plain,
! [P_48,Q_49] :
( is_a_theorem(implies(or(P_48,Q_49),or(Q_49,P_48)))
| ~ r3 ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_167,plain,
! [P_48,Q_49] : is_a_theorem(implies(or(P_48,Q_49),or(Q_49,P_48))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_132,plain,
r2,
inference(cnfTransformation,[status(thm)],[f_250]) ).
tff(c_98,plain,
! [Q_47,P_46] :
( is_a_theorem(implies(Q_47,or(P_46,Q_47)))
| ~ r2 ),
inference(cnfTransformation,[status(thm)],[f_155]) ).
tff(c_171,plain,
! [Q_47,P_46] : is_a_theorem(implies(Q_47,or(P_46,Q_47))),
inference(demodulation,[status(thm),theory(equality)],[c_132,c_98]) ).
tff(c_138,plain,
r5,
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_110,plain,
! [Q_54,R_55,P_53] :
( is_a_theorem(implies(implies(Q_54,R_55),implies(or(P_53,Q_54),or(P_53,R_55))))
| ~ r5 ),
inference(cnfTransformation,[status(thm)],[f_168]) ).
tff(c_1344,plain,
! [Q_180,R_181,P_182] : is_a_theorem(implies(implies(Q_180,R_181),implies(or(P_182,Q_180),or(P_182,R_181)))),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_110]) ).
tff(c_1353,plain,
! [Q_180,Y_63,X_62] : is_a_theorem(implies(implies(Q_180,Y_63),implies(or(not(X_62),Q_180),implies(X_62,Y_63)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_1344]) ).
tff(c_2156,plain,
! [Q_243,Y_244,X_245] : is_a_theorem(implies(implies(Q_243,Y_244),implies(implies(X_245,Q_243),implies(X_245,Y_244)))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_1353]) ).
tff(c_128,plain,
modus_ponens,
inference(cnfTransformation,[status(thm)],[f_247]) ).
tff(c_2,plain,
! [Y_2,X_1] :
( is_a_theorem(Y_2)
| ~ is_a_theorem(implies(X_1,Y_2))
| ~ is_a_theorem(X_1)
| ~ modus_ponens ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_190,plain,
! [Y_2,X_1] :
( is_a_theorem(Y_2)
| ~ is_a_theorem(implies(X_1,Y_2))
| ~ is_a_theorem(X_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_2834,plain,
! [X_291,Q_292,Y_293] :
( is_a_theorem(implies(implies(X_291,Q_292),implies(X_291,Y_293)))
| ~ is_a_theorem(implies(Q_292,Y_293)) ),
inference(resolution,[status(thm)],[c_2156,c_190]) ).
tff(c_320780,plain,
! [X_1977,Y_1978,Q_1979] :
( is_a_theorem(implies(X_1977,Y_1978))
| ~ is_a_theorem(implies(X_1977,Q_1979))
| ~ is_a_theorem(implies(Q_1979,Y_1978)) ),
inference(resolution,[status(thm)],[c_2834,c_190]) ).
tff(c_322183,plain,
! [Q_1982,Y_1983,P_1984] :
( is_a_theorem(implies(Q_1982,Y_1983))
| ~ is_a_theorem(implies(or(P_1984,Q_1982),Y_1983)) ),
inference(resolution,[status(thm)],[c_171,c_320780]) ).
tff(c_323152,plain,
! [Q_49,P_48] : is_a_theorem(implies(Q_49,or(Q_49,P_48))),
inference(resolution,[status(thm)],[c_167,c_322183]) ).
tff(c_44,plain,
( or_1
| ~ is_a_theorem(implies('#skF_20',or('#skF_20','#skF_21'))) ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_212,plain,
~ is_a_theorem(implies('#skF_20',or('#skF_20','#skF_21'))),
inference(splitLeft,[status(thm)],[c_44]) ).
tff(c_323163,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_323152,c_212]) ).
tff(c_323164,plain,
or_1,
inference(splitRight,[status(thm)],[c_44]) ).
tff(c_46,plain,
! [X_20,Y_21] :
( is_a_theorem(implies(X_20,or(X_20,Y_21)))
| ~ or_1 ),
inference(cnfTransformation,[status(thm)],[f_100]) ).
tff(c_323721,plain,
! [X_2041,Y_2042] : is_a_theorem(implies(X_2041,or(X_2041,Y_2042))),
inference(demodulation,[status(thm),theory(equality)],[c_323164,c_46]) ).
tff(c_323724,plain,
! [X_62,Y_63] : is_a_theorem(implies(not(X_62),implies(X_62,Y_63))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_323721]) ).
tff(c_142,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_261]) ).
tff(c_112,plain,
! [X_56,Y_57] :
( ( not(and(not(X_56),not(Y_57))) = or(X_56,Y_57) )
| ~ op_or ),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_157,plain,
! [X_56,Y_57] : ( not(and(not(X_56),not(Y_57))) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_112]) ).
tff(c_323719,plain,
! [X_20,Y_21] : is_a_theorem(implies(X_20,or(X_20,Y_21))),
inference(demodulation,[status(thm),theory(equality)],[c_323164,c_46]) ).
tff(c_136,plain,
r4,
inference(cnfTransformation,[status(thm)],[f_253]) ).
tff(c_106,plain,
! [P_50,Q_51,R_52] :
( is_a_theorem(implies(or(P_50,or(Q_51,R_52)),or(Q_51,or(P_50,R_52))))
| ~ r4 ),
inference(cnfTransformation,[status(thm)],[f_164]) ).
tff(c_324375,plain,
! [P_2107,Q_2108,R_2109] : is_a_theorem(implies(or(P_2107,or(Q_2108,R_2109)),or(Q_2108,or(P_2107,R_2109)))),
inference(demodulation,[status(thm),theory(equality)],[c_136,c_106]) ).
tff(c_324392,plain,
! [X_62,Q_2108,Y_63] : is_a_theorem(implies(or(not(X_62),or(Q_2108,Y_63)),or(Q_2108,implies(X_62,Y_63)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_324375]) ).
tff(c_325435,plain,
! [X_2178,Q_2179,Y_2180] : is_a_theorem(implies(implies(X_2178,or(Q_2179,Y_2180)),or(Q_2179,implies(X_2178,Y_2180)))),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_324392]) ).
tff(c_331178,plain,
! [Q_2511,X_2512,Y_2513] :
( is_a_theorem(or(Q_2511,implies(X_2512,Y_2513)))
| ~ is_a_theorem(implies(X_2512,or(Q_2511,Y_2513))) ),
inference(resolution,[status(thm)],[c_325435,c_190]) ).
tff(c_323726,plain,
! [Y_2045,X_2046] :
( is_a_theorem(Y_2045)
| ~ is_a_theorem(implies(X_2046,Y_2045))
| ~ is_a_theorem(X_2046) ),
inference(demodulation,[status(thm),theory(equality)],[c_128,c_2]) ).
tff(c_323750,plain,
! [P_46,Q_47] :
( is_a_theorem(or(P_46,Q_47))
| ~ is_a_theorem(Q_47) ),
inference(resolution,[status(thm)],[c_171,c_323726]) ).
tff(c_325134,plain,
! [Q_2161,P_2162,R_2163] :
( is_a_theorem(or(Q_2161,or(P_2162,R_2163)))
| ~ is_a_theorem(or(P_2162,or(Q_2161,R_2163))) ),
inference(resolution,[status(thm)],[c_324375,c_190]) ).
tff(c_325618,plain,
! [Q_2192,P_2193,R_2194] :
( is_a_theorem(or(Q_2192,or(P_2193,R_2194)))
| ~ is_a_theorem(or(Q_2192,R_2194)) ),
inference(resolution,[status(thm)],[c_323750,c_325134]) ).
tff(c_325637,plain,
! [X_62,P_2193,R_2194] :
( is_a_theorem(implies(X_62,or(P_2193,R_2194)))
| ~ is_a_theorem(or(not(X_62),R_2194)) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_325618]) ).
tff(c_325894,plain,
! [X_2212,P_2213,R_2214] :
( is_a_theorem(implies(X_2212,or(P_2213,R_2214)))
| ~ is_a_theorem(implies(X_2212,R_2214)) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_325637]) ).
tff(c_326339,plain,
! [P_2237,R_2238,X_2239] :
( is_a_theorem(or(P_2237,R_2238))
| ~ is_a_theorem(X_2239)
| ~ is_a_theorem(implies(X_2239,R_2238)) ),
inference(resolution,[status(thm)],[c_325894,c_190]) ).
tff(c_327084,plain,
! [P_2282,Q_2283,P_2284] :
( is_a_theorem(or(P_2282,or(Q_2283,P_2284)))
| ~ is_a_theorem(or(P_2284,Q_2283)) ),
inference(resolution,[status(thm)],[c_167,c_326339]) ).
tff(c_324398,plain,
! [Q_2108,P_2107,R_2109] :
( is_a_theorem(or(Q_2108,or(P_2107,R_2109)))
| ~ is_a_theorem(or(P_2107,or(Q_2108,R_2109))) ),
inference(resolution,[status(thm)],[c_324375,c_190]) ).
tff(c_327745,plain,
! [Q_2311,P_2312,P_2313] :
( is_a_theorem(or(Q_2311,or(P_2312,P_2313)))
| ~ is_a_theorem(or(P_2313,Q_2311)) ),
inference(resolution,[status(thm)],[c_327084,c_324398]) ).
tff(c_130,plain,
r1,
inference(cnfTransformation,[status(thm)],[f_249]) ).
tff(c_94,plain,
! [P_45] :
( is_a_theorem(implies(or(P_45,P_45),P_45))
| ~ r1 ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_175,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_94]) ).
tff(c_323749,plain,
! [P_45] :
( is_a_theorem(P_45)
| ~ is_a_theorem(or(P_45,P_45)) ),
inference(resolution,[status(thm)],[c_175,c_323726]) ).
tff(c_329625,plain,
! [P_2421,P_2422] :
( is_a_theorem(or(P_2421,P_2422))
| ~ is_a_theorem(or(P_2422,or(P_2421,P_2422))) ),
inference(resolution,[status(thm)],[c_327745,c_323749]) ).
tff(c_329714,plain,
! [X_62,Y_63] :
( is_a_theorem(or(not(X_62),Y_63))
| ~ is_a_theorem(or(Y_63,implies(X_62,Y_63))) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_329625]) ).
tff(c_329742,plain,
! [X_62,Y_63] :
( is_a_theorem(implies(X_62,Y_63))
| ~ is_a_theorem(or(Y_63,implies(X_62,Y_63))) ),
inference(demodulation,[status(thm),theory(equality)],[c_153,c_329714]) ).
tff(c_331425,plain,
! [X_2531,Y_2532] :
( is_a_theorem(implies(X_2531,Y_2532))
| ~ is_a_theorem(implies(X_2531,or(Y_2532,Y_2532))) ),
inference(resolution,[status(thm)],[c_331178,c_329742]) ).
tff(c_331552,plain,
! [Y_2533] : is_a_theorem(implies(Y_2533,Y_2533)),
inference(resolution,[status(thm)],[c_323719,c_331425]) ).
tff(c_323857,plain,
! [P_2059,Q_2060] : is_a_theorem(implies(or(P_2059,Q_2060),or(Q_2060,P_2059))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_324015,plain,
! [X_2068,Y_2069] : is_a_theorem(implies(implies(X_2068,Y_2069),or(Y_2069,not(X_2068)))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_323857]) ).
tff(c_324046,plain,
! [Y_2072,X_2073] :
( is_a_theorem(or(Y_2072,not(X_2073)))
| ~ is_a_theorem(implies(X_2073,Y_2072)) ),
inference(resolution,[status(thm)],[c_324015,c_190]) ).
tff(c_324062,plain,
! [X_62,X_2073] :
( is_a_theorem(implies(X_62,not(X_2073)))
| ~ is_a_theorem(implies(X_2073,not(X_62))) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_324046]) ).
tff(c_331588,plain,
! [X_62] : is_a_theorem(implies(X_62,not(not(X_62)))),
inference(resolution,[status(thm)],[c_331552,c_324062]) ).
tff(c_124,plain,
op_and,
inference(cnfTransformation,[status(thm)],[f_244]) ).
tff(c_114,plain,
! [X_58,Y_59] :
( ( not(or(not(X_58),not(Y_59))) = and(X_58,Y_59) )
| ~ op_and ),
inference(cnfTransformation,[status(thm)],[f_202]) ).
tff(c_155,plain,
! [X_58,Y_59] : ( not(implies(X_58,not(Y_59))) = and(X_58,Y_59) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_331825,plain,
! [X_2546] : is_a_theorem(implies(X_2546,not(not(X_2546)))),
inference(resolution,[status(thm)],[c_331552,c_324062]) ).
tff(c_332014,plain,
! [X_2550] :
( is_a_theorem(not(not(X_2550)))
| ~ is_a_theorem(X_2550) ),
inference(resolution,[status(thm)],[c_331825,c_190]) ).
tff(c_333736,plain,
! [X_2604,Y_2605] :
( is_a_theorem(not(and(X_2604,Y_2605)))
| ~ is_a_theorem(implies(X_2604,not(Y_2605))) ),
inference(superposition,[status(thm),theory(equality)],[c_155,c_332014]) ).
tff(c_333831,plain,
! [X_2606] : is_a_theorem(not(and(X_2606,not(X_2606)))),
inference(resolution,[status(thm)],[c_331588,c_333736]) ).
tff(c_333857,plain,
! [X_2607] : is_a_theorem(or(X_2607,not(X_2607))),
inference(superposition,[status(thm),theory(equality)],[c_157,c_333831]) ).
tff(c_324293,plain,
! [Q_2099,R_2100,P_2101] : is_a_theorem(implies(implies(Q_2099,R_2100),implies(or(P_2101,Q_2099),or(P_2101,R_2100)))),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_110]) ).
tff(c_326098,plain,
! [P_2220,Q_2221,R_2222] :
( is_a_theorem(implies(or(P_2220,Q_2221),or(P_2220,R_2222)))
| ~ is_a_theorem(implies(Q_2221,R_2222)) ),
inference(resolution,[status(thm)],[c_324293,c_190]) ).
tff(c_326113,plain,
! [P_2220,R_2222,Q_2221] :
( is_a_theorem(or(P_2220,R_2222))
| ~ is_a_theorem(or(P_2220,Q_2221))
| ~ is_a_theorem(implies(Q_2221,R_2222)) ),
inference(resolution,[status(thm)],[c_326098,c_190]) ).
tff(c_335351,plain,
! [X_2674,R_2675] :
( is_a_theorem(or(X_2674,R_2675))
| ~ is_a_theorem(implies(not(X_2674),R_2675)) ),
inference(resolution,[status(thm)],[c_333857,c_326113]) ).
tff(c_335536,plain,
! [X_2676,Y_2677] : is_a_theorem(or(X_2676,implies(X_2676,Y_2677))),
inference(resolution,[status(thm)],[c_323724,c_335351]) ).
tff(c_335565,plain,
! [X_62,Y_2677] : is_a_theorem(implies(X_62,implies(not(X_62),Y_2677))),
inference(superposition,[status(thm),theory(equality)],[c_153,c_335536]) ).
tff(c_148,plain,
~ cn2,
inference(cnfTransformation,[status(thm)],[f_265]) ).
tff(c_84,plain,
( cn2
| ~ is_a_theorem(implies('#skF_42',implies(not('#skF_42'),'#skF_43'))) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_178,plain,
~ is_a_theorem(implies('#skF_42',implies(not('#skF_42'),'#skF_43'))),
inference(negUnitSimplification,[status(thm)],[c_148,c_84]) ).
tff(c_335672,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_335565,c_178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL497+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n025.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 : Thu Aug 3 13:45:34 EDT 2023
% 0.13/0.34 % CPUTime :
% 113.66/83.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 113.66/83.50
% 113.66/83.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 113.66/83.54
% 113.66/83.54 Inference rules
% 113.66/83.54 ----------------------
% 113.66/83.54 #Ref : 0
% 113.66/83.54 #Sup : 93438
% 113.66/83.54 #Fact : 0
% 113.66/83.54 #Define : 0
% 113.66/83.54 #Split : 85
% 113.66/83.54 #Chain : 0
% 113.66/83.54 #Close : 0
% 113.66/83.54
% 113.66/83.54 Ordering : KBO
% 113.66/83.54
% 113.66/83.54 Simplification rules
% 113.66/83.54 ----------------------
% 113.66/83.54 #Subsume : 14600
% 113.66/83.54 #Demod : 49249
% 113.66/83.54 #Tautology : 20014
% 113.66/83.54 #SimpNegUnit : 570
% 113.66/83.54 #BackRed : 27
% 113.66/83.54
% 113.66/83.54 #Partial instantiations: 0
% 113.66/83.54 #Strategies tried : 1
% 113.66/83.54
% 113.66/83.54 Timing (in seconds)
% 113.66/83.54 ----------------------
% 113.66/83.55 Preprocessing : 0.61
% 113.66/83.55 Parsing : 0.32
% 113.66/83.55 CNF conversion : 0.05
% 113.66/83.55 Main loop : 81.85
% 113.66/83.55 Inferencing : 5.26
% 113.66/83.55 Reduction : 45.22
% 113.66/83.55 Demodulation : 35.53
% 113.66/83.55 BG Simplification : 0.64
% 113.90/83.55 Subsumption : 25.37
% 113.90/83.55 Abstraction : 0.98
% 113.90/83.55 MUC search : 0.00
% 113.90/83.55 Cooper : 0.00
% 113.90/83.55 Total : 82.53
% 113.90/83.55 Index Insertion : 0.00
% 113.90/83.55 Index Deletion : 0.00
% 113.90/83.55 Index Matching : 0.00
% 113.90/83.55 BG Taut test : 0.00
%------------------------------------------------------------------------------