%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:11:59 AM UTC 2026
% Result : Theorem 9.64s 3.89s
% Output : CNFRefutation 10.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 51 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 77 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 22 ~; 16 |; 1 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 50 ( 50 !; 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_254,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
tff(f_77,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
tff(f_255,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
tff(f_81,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
tff(f_251,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
tff(f_61,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_262,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
tff(f_109,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_3) ).
tff(f_152,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
tff(f_276,negated_conjecture,
~ cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).
tff(f_272,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_op_or) ).
tff(f_248,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
tff(f_207,axiom,
( op_implies_and
=> ! [X,Y] : ( implies(X,Y) = not(and(X,not(Y))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
tff(f_199,axiom,
( op_or
=> ! [X,Y] : ( or(X,Y) = not(and(not(X),not(Y))) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
tff(f_147,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).
tff(c_132,plain,
implies_1,
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_22,plain,
! [X_7,Y_8] :
( is_a_theorem(implies(X_7,implies(Y_8,X_7)))
| ~ implies_1 ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_237,plain,
! [X_7,Y_8] : is_a_theorem(implies(X_7,implies(Y_8,X_7))),
inference(demodulation,[status(thm),theory(equality)],[c_132,c_22]) ).
tff(c_134,plain,
implies_2,
inference(cnfTransformation,[status(thm)],[f_255]) ).
tff(c_26,plain,
! [X_9,Y_10] :
( is_a_theorem(implies(implies(X_9,implies(X_9,Y_10)),implies(X_9,Y_10)))
| ~ implies_2 ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_1458,plain,
! [X_251,Y_252] : is_a_theorem(implies(implies(X_251,implies(X_251,Y_252)),implies(X_251,Y_252))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_26]) ).
tff(c_128,plain,
modus_ponens,
inference(cnfTransformation,[status(thm)],[f_251]) ).
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_61]) ).
tff(c_252,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_1912,plain,
! [X_299,Y_300] :
( is_a_theorem(implies(X_299,Y_300))
| ~ is_a_theorem(implies(X_299,implies(X_299,Y_300))) ),
inference(resolution,[status(thm)],[c_1458,c_252]) ).
tff(c_1968,plain,
! [Y_8] : is_a_theorem(implies(Y_8,Y_8)),
inference(resolution,[status(thm)],[c_237,c_1912]) ).
tff(c_148,plain,
or_3,
inference(cnfTransformation,[status(thm)],[f_262]) ).
tff(c_54,plain,
! [X_24,Z_26,Y_25] :
( is_a_theorem(implies(implies(X_24,Z_26),implies(implies(Y_25,Z_26),implies(or(X_24,Y_25),Z_26))))
| ~ or_3 ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_193,plain,
! [X_24,Z_26,Y_25] : is_a_theorem(implies(implies(X_24,Z_26),implies(implies(Y_25,Z_26),implies(or(X_24,Y_25),Z_26)))),
inference(demodulation,[status(thm),theory(equality)],[c_148,c_54]) ).
tff(c_2140,plain,
! [Y_329,Z_330] : is_a_theorem(implies(implies(Y_329,Z_330),implies(or(Y_329,Y_329),Z_330))),
inference(resolution,[status(thm)],[c_193,c_1912]) ).
tff(c_2326,plain,
! [Y_336,Z_337] :
( is_a_theorem(implies(or(Y_336,Y_336),Z_337))
| ~ is_a_theorem(implies(Y_336,Z_337)) ),
inference(resolution,[status(thm)],[c_2140,c_252]) ).
tff(c_92,plain,
( r1
| ~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')) ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_1081,plain,
~ is_a_theorem(implies(or('#skF_45','#skF_45'),'#skF_45')),
inference(splitLeft,[status(thm)],[c_92]) ).
tff(c_2339,plain,
~ is_a_theorem(implies('#skF_45','#skF_45')),
inference(resolution,[status(thm)],[c_2326,c_1081]) ).
tff(c_2353,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1968,c_2339]) ).
tff(c_2354,plain,
r1,
inference(splitRight,[status(thm)],[c_92]) ).
tff(c_94,plain,
! [P_45] :
( is_a_theorem(implies(or(P_45,P_45),P_45))
| ~ r1 ),
inference(cnfTransformation,[status(thm)],[f_152]) ).
tff(c_2356,plain,
~ r1,
inference(splitLeft,[status(thm)],[c_94]) ).
tff(c_2358,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2354,c_2356]) ).
tff(c_2359,plain,
! [P_45] : is_a_theorem(implies(or(P_45,P_45),P_45)),
inference(splitRight,[status(thm)],[c_94]) ).
tff(c_164,plain,
~ cn3,
inference(cnfTransformation,[status(thm)],[f_276]) ).
tff(c_158,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_272]) ).
tff(c_124,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_248]) ).
tff(c_116,plain,
! [X_60,Y_61] :
( ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) )
| ~ op_implies_and ),
inference(cnfTransformation,[status(thm)],[f_207]) ).
tff(c_170,plain,
! [X_60,Y_61] : ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_116]) ).
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_199]) ).
tff(c_172,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_158,c_170,c_112]) ).
tff(c_88,plain,
( cn3
| ~ is_a_theorem(implies(implies(not('#skF_44'),'#skF_44'),'#skF_44')) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_174,plain,
( cn3
| ~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')) ),
inference(demodulation,[status(thm),theory(equality)],[c_172,c_88]) ).
tff(c_175,plain,
~ is_a_theorem(implies(or('#skF_44','#skF_44'),'#skF_44')),
inference(negUnitSimplification,[status(thm)],[c_164,c_174]) ).
tff(c_2368,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2359,c_175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 5 12:41:11 UTC 2026
% 0.12/0.38 % CPUTime :
% 9.64/3.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.06/3.90
% 10.06/3.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------