%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL069-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% 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 : n019.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 11:11:10 AM UTC 2026
% Result : Unsatisfiable 11.55s 4.49s
% Output : CNFRefutation 11.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 72 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > not > b > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(b,type,
b: $i ).
tff(not,type,
not: $i > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_39,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))),
file(unknown,unknown) ).
tff(f_37,axiom,
! [X,Y] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_41,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))),
file(unknown,unknown) ).
tff(f_43,axiom,
! [X,Z,Y] : is_a_theorem(implies(implies(not(X),Z),implies(implies(Y,Z),implies(implies(X,Y),Z)))),
file(unknown,unknown) ).
tff(f_45,axiom,
~ is_a_theorem(implies(a,implies(not(a),b))),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4,Z_5] : is_a_theorem(implies(implies(implies(X_3,Y_4),Z_5),implies(Y_4,Z_5))),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_12,plain,
! [X_14,Y_15,Z_16] : is_a_theorem(implies(implies(implies(X_14,Y_15),Z_16),implies(Y_15,Z_16))),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_2,plain,
! [Y_2,X_1] :
( is_a_theorem(Y_2)
| ~ is_a_theorem(X_1)
| ~ is_a_theorem(implies(X_1,Y_2)) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_17,plain,
! [Y_17,Z_18,X_19] :
( is_a_theorem(implies(Y_17,Z_18))
| ~ is_a_theorem(implies(implies(X_19,Y_17),Z_18)) ),
inference(resolution,[status(thm)],[c_12,c_2]) ).
tff(c_22,plain,
! [Z_20,Y_21] : is_a_theorem(implies(Z_20,implies(Y_21,Z_20))),
inference(resolution,[status(thm)],[c_4,c_17]) ).
tff(c_16,plain,
! [Y_15,Z_16,X_14] :
( is_a_theorem(implies(Y_15,Z_16))
| ~ is_a_theorem(implies(implies(X_14,Y_15),Z_16)) ),
inference(resolution,[status(thm)],[c_12,c_2]) ).
tff(c_30,plain,
! [Y_15,Y_21,X_14] : is_a_theorem(implies(Y_15,implies(Y_21,implies(X_14,Y_15)))),
inference(resolution,[status(thm)],[c_22,c_16]) ).
tff(c_32,plain,
! [X_22,Y_23,Z_24] : is_a_theorem(implies(implies(implies(X_22,Y_23),Z_24),implies(not(X_22),Z_24))),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_113,plain,
! [X_44,Z_45,Y_46] :
( is_a_theorem(implies(not(X_44),Z_45))
| ~ is_a_theorem(implies(implies(X_44,Y_46),Z_45)) ),
inference(resolution,[status(thm)],[c_32,c_2]) ).
tff(c_150,plain,
! [X_44,Y_21,X_14,Y_46] : is_a_theorem(implies(not(X_44),implies(Y_21,implies(X_14,implies(X_44,Y_46))))),
inference(resolution,[status(thm)],[c_30,c_113]) ).
tff(c_21,plain,
! [Z_5,Y_4] : is_a_theorem(implies(Z_5,implies(Y_4,Z_5))),
inference(resolution,[status(thm)],[c_4,c_17]) ).
tff(c_154,plain,
! [X_44,Y_4,Y_46] : is_a_theorem(implies(not(X_44),implies(Y_4,implies(X_44,Y_46)))),
inference(resolution,[status(thm)],[c_21,c_113]) ).
tff(c_60,plain,
! [X_27,Z_28,Y_29] : is_a_theorem(implies(implies(not(X_27),Z_28),implies(implies(Y_29,Z_28),implies(implies(X_27,Y_29),Z_28)))),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_156,plain,
! [Y_47,Z_48,X_49] :
( is_a_theorem(implies(implies(Y_47,Z_48),implies(implies(X_49,Y_47),Z_48)))
| ~ is_a_theorem(implies(not(X_49),Z_48)) ),
inference(resolution,[status(thm)],[c_60,c_2]) ).
tff(c_460,plain,
! [X_119,Y_120,Z_121] :
( is_a_theorem(implies(implies(X_119,Y_120),Z_121))
| ~ is_a_theorem(implies(Y_120,Z_121))
| ~ is_a_theorem(implies(not(X_119),Z_121)) ),
inference(resolution,[status(thm)],[c_156,c_2]) ).
tff(c_484,plain,
! [Z_136,X_137,Y_138] :
( is_a_theorem(Z_136)
| ~ is_a_theorem(implies(X_137,Y_138))
| ~ is_a_theorem(implies(Y_138,Z_136))
| ~ is_a_theorem(implies(not(X_137),Z_136)) ),
inference(resolution,[status(thm)],[c_460,c_2]) ).
tff(c_2373,plain,
! [Z_224,Y_225,X_226,Y_227] :
( is_a_theorem(Z_224)
| ~ is_a_theorem(implies(implies(Y_225,implies(X_226,Y_227)),Z_224))
| ~ is_a_theorem(implies(not(not(X_226)),Z_224)) ),
inference(resolution,[status(thm)],[c_154,c_484]) ).
tff(c_10988,plain,
! [Y_557,X_558,Y_559] :
( is_a_theorem(implies(Y_557,implies(X_558,Y_559)))
| ~ is_a_theorem(implies(not(not(X_558)),implies(Y_557,implies(X_558,Y_559)))) ),
inference(resolution,[status(thm)],[c_4,c_2373]) ).
tff(c_11330,plain,
! [Y_562,X_563,Y_564] : is_a_theorem(implies(Y_562,implies(X_563,implies(not(X_563),Y_564)))),
inference(resolution,[status(thm)],[c_150,c_10988]) ).
tff(c_2503,plain,
! [Y_4,X_226,Y_227] :
( is_a_theorem(implies(Y_4,implies(X_226,Y_227)))
| ~ is_a_theorem(implies(not(not(X_226)),implies(Y_4,implies(X_226,Y_227)))) ),
inference(resolution,[status(thm)],[c_4,c_2373]) ).
tff(c_11455,plain,
! [X_563,Y_564] : is_a_theorem(implies(X_563,implies(not(X_563),Y_564))),
inference(resolution,[status(thm)],[c_11330,c_2503]) ).
tff(c_10,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_11525,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_11455,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL069-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% 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
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 5 03:55:08 UTC 2026
% 0.10/0.38 % CPUTime :
% 11.55/4.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.76/4.50
% 11.76/4.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------