%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL494+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 : n018.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 11:12:03 AM UTC 2026
% Result : Theorem 15.21s 5.24s
% Output : CNFRefutation 15.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 61 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 20 ~; 16 |; 1 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 ( 32 usr; 32 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 55 con; 0-2 aty)
% Number of variables : 73 ( 73 !; 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_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(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_266,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
tff(f_215,axiom,
( op_equiv
=> ! [X,Y] : ( equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
tff(f_247,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
tff(f_246,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
tff(f_211,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_203,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_264,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
tff(f_265,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
tff(f_207,axiom,
( op_implies_and
=> ! [X,Y] : ( implies(X,Y) = not(and(X,not(Y))) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
tff(f_253,axiom,
r2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
tff(f_156,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,
r3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
tff(f_160,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,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
tff(f_93,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_2) ).
tff(f_268,negated_conjecture,
~ equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
tff(f_117,axiom,
( equivalence_2
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',equivalence_2) ).
tff(c_146,plain,
op_equiv,
inference(cnfTransformation,[status(thm)],[f_266]) ).
tff(c_120,plain,
! [X_64,Y_65] :
( ( and(implies(X_64,Y_65),implies(Y_65,X_64)) = equiv(X_64,Y_65) )
| ~ op_equiv ),
inference(cnfTransformation,[status(thm)],[f_215]) ).
tff(c_6616,plain,
! [X_474,Y_475] : ( and(implies(X_474,Y_475),implies(Y_475,X_474)) = equiv(X_474,Y_475) ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_120]) ).
tff(c_124,plain,
op_and,
inference(cnfTransformation,[status(thm)],[f_247]) ).
tff(c_122,plain,
op_implies_or,
inference(cnfTransformation,[status(thm)],[f_246]) ).
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_211]) ).
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_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_203]) ).
tff(c_2549,plain,
! [X_245,Y_246] : ( not(implies(X_245,not(Y_246))) = and(X_245,Y_246) ),
inference(demodulation,[status(thm),theory(equality)],[c_124,c_153,c_114]) ).
tff(c_142,plain,
op_or,
inference(cnfTransformation,[status(thm)],[f_264]) ).
tff(c_144,plain,
op_implies_and,
inference(cnfTransformation,[status(thm)],[f_265]) ).
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_155,plain,
! [X_60,Y_61] : ( not(and(X_60,not(Y_61))) = implies(X_60,Y_61) ),
inference(demodulation,[status(thm),theory(equality)],[c_144,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_159,plain,
! [X_56,Y_57] : ( implies(not(X_56),Y_57) = or(X_56,Y_57) ),
inference(demodulation,[status(thm),theory(equality)],[c_142,c_155,c_112]) ).
tff(c_2570,plain,
! [X_245,Y_246,Y_57] : ( or(implies(X_245,not(Y_246)),Y_57) = implies(and(X_245,Y_246),Y_57) ),
inference(superposition,[status(thm),theory(equality)],[c_2549,c_159]) ).
tff(c_2471,plain,
! [X_235,Y_236] : ( or(not(X_235),Y_236) = implies(X_235,Y_236) ),
inference(demodulation,[status(thm),theory(equality)],[c_122,c_118]) ).
tff(c_132,plain,
r2,
inference(cnfTransformation,[status(thm)],[f_253]) ).
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_156]) ).
tff(c_173,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_2488,plain,
! [Y_237,X_238] : is_a_theorem(implies(Y_237,implies(X_238,Y_237))),
inference(superposition,[status(thm),theory(equality)],[c_2471,c_173]) ).
tff(c_2495,plain,
! [X_56,X_238] : is_a_theorem(or(X_56,implies(X_238,not(X_56)))),
inference(superposition,[status(thm),theory(equality)],[c_159,c_2488]) ).
tff(c_134,plain,
r3,
inference(cnfTransformation,[status(thm)],[f_254]) ).
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_160]) ).
tff(c_2654,plain,
! [P_255,Q_256] : is_a_theorem(implies(or(P_255,Q_256),or(Q_256,P_255))),
inference(demodulation,[status(thm),theory(equality)],[c_134,c_102]) ).
tff(c_128,plain,
modus_ponens,
inference(cnfTransformation,[status(thm)],[f_250]) ).
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_201,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_2741,plain,
! [Q_259,P_260] :
( is_a_theorem(or(Q_259,P_260))
| ~ is_a_theorem(or(P_260,Q_259)) ),
inference(resolution,[status(thm)],[c_2654,c_201]) ).
tff(c_2754,plain,
! [X_238,X_56] : is_a_theorem(or(implies(X_238,not(X_56)),X_56)),
inference(resolution,[status(thm)],[c_2495,c_2741]) ).
tff(c_5872,plain,
! [X_238,X_56] : is_a_theorem(implies(and(X_238,X_56),X_56)),
inference(demodulation,[status(thm),theory(equality)],[c_2570,c_2754]) ).
tff(c_36,plain,
( and_2
| ~ is_a_theorem(implies(and('#skF_16','#skF_17'),'#skF_17')) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_207,plain,
~ is_a_theorem(implies(and('#skF_16','#skF_17'),'#skF_17')),
inference(splitLeft,[status(thm)],[c_36]) ).
tff(c_6081,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5872,c_207]) ).
tff(c_6082,plain,
and_2,
inference(splitRight,[status(thm)],[c_36]) ).
tff(c_38,plain,
! [X_16,Y_17] :
( is_a_theorem(implies(and(X_16,Y_17),Y_17))
| ~ and_2 ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_6100,plain,
! [X_16,Y_17] : is_a_theorem(implies(and(X_16,Y_17),Y_17)),
inference(demodulation,[status(thm),theory(equality)],[c_6082,c_38]) ).
tff(c_6625,plain,
! [X_474,Y_475] : is_a_theorem(implies(equiv(X_474,Y_475),implies(Y_475,X_474))),
inference(superposition,[status(thm),theory(equality)],[c_6616,c_6100]) ).
tff(c_148,plain,
~ equivalence_2,
inference(cnfTransformation,[status(thm)],[f_268]) ).
tff(c_60,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv('#skF_29','#skF_30'),implies('#skF_30','#skF_29'))) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_187,plain,
~ is_a_theorem(implies(equiv('#skF_29','#skF_30'),implies('#skF_30','#skF_29'))),
inference(negUnitSimplification,[status(thm)],[c_148,c_60]) ).
tff(c_6650,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6625,c_187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL494+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
% 0.12/0.38 % Computer : n018.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 : Fri Sep 4 19:03:17 UTC 2026
% 0.12/0.38 % CPUTime :
% 15.21/5.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.21/5.25
% 15.21/5.25 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------