%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL113-2 : TPTP v9.3.1. Released v1.0.0.
% 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 : n028.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 11:11:17 AM UTC 2026
% Result : Unsatisfiable 11.79s 4.58s
% Output : CNFRefutation 12.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 72 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ implies > #nlpp > not > y > x > truth
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(truth,type,
truth: $i ).
tff(x,type,
x: $i ).
tff(y,type,
y: $i ).
tff(not,type,
not: $i > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_51,axiom,
! [X] : ( implies(truth,X) = X ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file(unknown,unknown) ).
tff(f_55,axiom,
! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Y] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
file(unknown,unknown) ).
tff(f_61,axiom,
implies(implies(not(x),y),implies(not(y),x)) != truth,
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : ( implies(truth,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_187,plain,
! [X_17,Y_18,Z_19] : ( implies(implies(X_17,Y_18),implies(implies(Y_18,Z_19),implies(X_17,Z_19))) = truth ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_308,plain,
! [X_1,Z_19] : ( implies(X_1,implies(implies(X_1,Z_19),implies(truth,Z_19))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_187]) ).
tff(c_408,plain,
! [X_21,Z_22] : ( implies(X_21,implies(implies(X_21,Z_22),Z_22)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_308]) ).
tff(c_439,plain,
! [Z_22] : ( implies(implies(truth,Z_22),Z_22) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_408,c_2]) ).
tff(c_503,plain,
! [Z_22] : ( implies(Z_22,Z_22) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_439]) ).
tff(c_46,plain,
! [Y_13,X_14] : ( implies(implies(Y_13,X_14),X_14) = implies(implies(X_14,Y_13),Y_13) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_79,plain,
! [X_1] : ( implies(implies(X_1,truth),truth) = implies(X_1,X_1) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_46]) ).
tff(c_571,plain,
! [X_24] : ( implies(implies(X_24,truth),truth) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_503,c_79]) ).
tff(c_326,plain,
! [X_1,Z_19] : ( implies(X_1,implies(implies(X_1,Z_19),Z_19)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_308]) ).
tff(c_656,plain,
! [X_25] : ( implies(X_25,truth) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_571,c_326]) ).
tff(c_4,plain,
! [X_2,Y_3,Z_4] : ( implies(implies(X_2,Y_3),implies(implies(Y_3,Z_4),implies(X_2,Z_4))) = truth ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_670,plain,
! [Z_4,X_25] : ( implies(truth,implies(implies(truth,Z_4),implies(X_25,Z_4))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_656,c_4]) ).
tff(c_725,plain,
! [Z_4,X_25] : ( implies(Z_4,implies(X_25,Z_4)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_670]) ).
tff(c_8,plain,
! [X_7,Y_8] : ( implies(implies(not(X_7),not(Y_8)),implies(Y_8,X_7)) = truth ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_298,plain,
! [X_17,X_7,Y_8] : ( implies(implies(X_17,implies(not(X_7),not(Y_8))),implies(truth,implies(X_17,implies(Y_8,X_7)))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_187]) ).
tff(c_860,plain,
! [X_28,X_29,Y_30] : ( implies(implies(X_28,implies(not(X_29),not(Y_30))),implies(X_28,implies(Y_30,X_29))) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_298]) ).
tff(c_1017,plain,
! [Y_31,X_32] : ( implies(truth,implies(not(Y_31),implies(Y_31,X_32))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_725,c_860]) ).
tff(c_1034,plain,
! [Y_31,X_32] : ( implies(truth,implies(truth,implies(not(Y_31),implies(Y_31,X_32)))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1017,c_326]) ).
tff(c_1125,plain,
! [Y_33,X_34] : ( implies(not(Y_33),implies(Y_33,X_34)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_1034]) ).
tff(c_1208,plain,
! [X_1] : ( implies(not(truth),X_1) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1125]) ).
tff(c_20,plain,
! [X_10,Y_11] : ( implies(implies(not(X_10),not(Y_11)),implies(Y_11,X_10)) = truth ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_33,plain,
! [X_1] : ( implies(implies(not(X_1),not(truth)),X_1) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_20]) ).
tff(c_1232,plain,
! [X_35] : ( implies(not(truth),X_35) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1125]) ).
tff(c_6,plain,
! [Y_6,X_5] : ( implies(implies(Y_6,X_5),X_5) = implies(implies(X_5,Y_6),Y_6) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_1288,plain,
! [X_35] : ( implies(implies(X_35,not(truth)),not(truth)) = implies(truth,X_35) ),
inference(superposition,[status(thm),theory(equality)],[c_1232,c_6]) ).
tff(c_1349,plain,
! [X_36] : ( implies(implies(X_36,not(truth)),not(truth)) = X_36 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1288]) ).
tff(c_1389,plain,
not(not(truth)) = truth,
inference(superposition,[status(thm),theory(equality)],[c_1349,c_33]) ).
tff(c_1334,plain,
! [X_35] : ( implies(implies(X_35,not(truth)),not(truth)) = X_35 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1288]) ).
tff(c_4246,plain,
! [Y_62,X_63,Z_64] : ( implies(truth,implies(implies(implies(Y_62,X_63),Z_64),implies(implies(not(X_63),not(Y_62)),Z_64))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_187]) ).
tff(c_4423,plain,
! [X_35] : ( implies(truth,implies(X_35,implies(implies(not(not(truth)),not(X_35)),not(truth)))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1334,c_4246]) ).
tff(c_4858,plain,
! [X_66] : ( implies(X_66,implies(not(X_66),not(truth))) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_1389,c_4423]) ).
tff(c_4950,plain,
! [X_66] : ( implies(implies(implies(not(X_66),not(truth)),X_66),X_66) = implies(truth,implies(not(X_66),not(truth))) ),
inference(superposition,[status(thm),theory(equality)],[c_4858,c_6]) ).
tff(c_5040,plain,
! [X_67] : ( implies(not(X_67),not(truth)) = X_67 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_33,c_2,c_4950]) ).
tff(c_5137,plain,
! [X_67] : ( implies(implies(not(truth),not(X_67)),not(X_67)) = implies(X_67,not(truth)) ),
inference(superposition,[status(thm),theory(equality)],[c_5040,c_6]) ).
tff(c_5190,plain,
! [X_67] : ( implies(X_67,not(truth)) = not(X_67) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_1208,c_5137]) ).
tff(c_6455,plain,
! [Y_76,X_77,Y_78] : ( implies(implies(implies(Y_76,X_77),Y_78),implies(implies(Y_78,X_77),implies(implies(X_77,Y_76),Y_76))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_187]) ).
tff(c_6732,plain,
! [X_1,Y_78] : ( implies(implies(implies(X_1,not(truth)),Y_78),implies(implies(Y_78,not(truth)),implies(truth,X_1))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_1208,c_6455]) ).
tff(c_6968,plain,
! [X_1,Y_78] : ( implies(implies(not(X_1),Y_78),implies(not(Y_78),X_1)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_5190,c_5190,c_2,c_6732]) ).
tff(c_10,plain,
implies(implies(not(x),y),implies(not(y),x)) != truth,
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_13136,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6968,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL113-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % 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
% 0.09/0.36 % Computer : n028.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 20:18:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 11.79/4.58 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.79/4.59
% 11.79/4.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------