%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL465+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/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 : n011.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 11:12:01 AM UTC 2026
% Result : Theorem 4.66s 2.48s
% Output : CNFRefutation 4.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 2 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 34 ( 33 usr; 33 prp; 0-1 aty)
% Number of functors : 60 ( 60 usr; 55 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 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_265,negated_conjecture,
~ implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
tff(f_252,axiom,
cn1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax',luka_cn1) ).
tff(f_139,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn1) ).
tff(f_85,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_3) ).
tff(c_144,plain,
~ implies_3,
inference(cnfTransformation,[status(thm)],[f_265]) ).
tff(c_130,plain,
cn1,
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_82,plain,
! [P_39,Q_40,R_41] :
( is_a_theorem(implies(implies(P_39,Q_40),implies(implies(Q_40,R_41),implies(P_39,R_41))))
| ~ cn1 ),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_165,plain,
! [P_39,Q_40,R_41] : is_a_theorem(implies(implies(P_39,Q_40),implies(implies(Q_40,R_41),implies(P_39,R_41)))),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_82]) ).
tff(c_28,plain,
( implies_3
| ~ is_a_theorem(implies(implies('#skF_11','#skF_12'),implies(implies('#skF_12','#skF_13'),implies('#skF_11','#skF_13')))) ),
inference(cnfTransformation,[status(thm)],[f_85]) ).
tff(c_175,plain,
implies_3,
inference(demodulation,[status(thm),theory(equality)],[c_165,c_28]) ).
tff(c_176,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_144,c_175]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL465+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % 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
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 21:20:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 4.66/2.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.66/2.49
% 4.66/2.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------