%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL039-1 : 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 : 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 11:11:07 AM UTC 2026
% Result : Unsatisfiable 16.95s 6.03s
% Output : CNFRefutation 16.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 28 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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; 1 con; 0-2 aty)
% Number of variables : 66 ( 66 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > not > necessary > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(not,type,
not: $i > $i ).
tff(necessary,type,
necessary: $i > $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_44,axiom,
! [X] : is_a_theorem(implies(necessary(X),X)),
file(unknown,unknown) ).
tff(f_36,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
file(unknown,unknown) ).
tff(f_34,axiom,
! [X,Y] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_40,axiom,
! [X,Y] : is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
file(unknown,unknown) ).
tff(f_38,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
file(unknown,unknown) ).
tff(f_51,axiom,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
file(unknown,unknown) ).
tff(c_12,plain,
! [X_12] : is_a_theorem(implies(necessary(X_12),X_12)),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_4,plain,
! [X_3,Y_4] : is_a_theorem(implies(X_3,implies(Y_4,X_3))),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_20,plain,
! [Y_18,X_19] :
( is_a_theorem(Y_18)
| ~ is_a_theorem(X_19)
| ~ is_a_theorem(implies(X_19,Y_18)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_27,plain,
! [Y_4,X_3] :
( is_a_theorem(implies(Y_4,X_3))
| ~ is_a_theorem(X_3) ),
inference(resolution,[status(thm)],[c_4,c_20]) ).
tff(c_8,plain,
! [X_8,Y_9] : is_a_theorem(implies(implies(not(X_8),not(Y_9)),implies(Y_9,X_8))),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_73,plain,
! [X_32,Y_33,Z_34] : is_a_theorem(implies(implies(X_32,implies(Y_33,Z_34)),implies(implies(X_32,Y_33),implies(X_32,Z_34)))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
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_34]) ).
tff(c_158,plain,
! [X_49,Y_50,Z_51] :
( is_a_theorem(implies(implies(X_49,Y_50),implies(X_49,Z_51)))
| ~ is_a_theorem(implies(X_49,implies(Y_50,Z_51))) ),
inference(resolution,[status(thm)],[c_73,c_2]) ).
tff(c_223,plain,
! [X_65,Z_66,Y_67] :
( is_a_theorem(implies(X_65,Z_66))
| ~ is_a_theorem(implies(X_65,Y_67))
| ~ is_a_theorem(implies(X_65,implies(Y_67,Z_66))) ),
inference(resolution,[status(thm)],[c_158,c_2]) ).
tff(c_964,plain,
! [X_131,Y_132] :
( is_a_theorem(implies(implies(not(X_131),not(Y_132)),X_131))
| ~ is_a_theorem(implies(implies(not(X_131),not(Y_132)),Y_132)) ),
inference(resolution,[status(thm)],[c_8,c_223]) ).
tff(c_992,plain,
! [X_131,X_3] :
( is_a_theorem(implies(implies(not(X_131),not(X_3)),X_131))
| ~ is_a_theorem(X_3) ),
inference(resolution,[status(thm)],[c_27,c_964]) ).
tff(c_347,plain,
! [Y_73,Z_74,Y_75] :
( is_a_theorem(implies(Y_73,Z_74))
| ~ is_a_theorem(implies(Y_73,Y_75))
| ~ is_a_theorem(implies(Y_75,Z_74)) ),
inference(resolution,[status(thm)],[c_27,c_223]) ).
tff(c_2741,plain,
! [X_238,Y_239,Z_240] :
( is_a_theorem(implies(implies(not(X_238),not(Y_239)),Z_240))
| ~ is_a_theorem(implies(implies(Y_239,X_238),Z_240)) ),
inference(resolution,[status(thm)],[c_8,c_347]) ).
tff(c_379,plain,
! [X_3,Z_74,Y_4] :
( is_a_theorem(implies(X_3,Z_74))
| ~ is_a_theorem(implies(implies(Y_4,X_3),Z_74)) ),
inference(resolution,[status(thm)],[c_4,c_347]) ).
tff(c_2871,plain,
! [Y_244,Z_245,X_246] :
( is_a_theorem(implies(not(Y_244),Z_245))
| ~ is_a_theorem(implies(implies(Y_244,X_246),Z_245)) ),
inference(resolution,[status(thm)],[c_2741,c_379]) ).
tff(c_2939,plain,
! [X_131,X_3] :
( is_a_theorem(implies(not(not(X_131)),X_131))
| ~ is_a_theorem(X_3) ),
inference(resolution,[status(thm)],[c_992,c_2871]) ).
tff(c_2954,plain,
! [X_3] : ~ is_a_theorem(X_3),
inference(splitLeft,[status(thm)],[c_2939]) ).
tff(c_2952,plain,
! [X_8,Y_9] : is_a_theorem(implies(not(not(X_8)),implies(Y_9,X_8))),
inference(resolution,[status(thm)],[c_8,c_2871]) ).
tff(c_3085,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2954,c_2952]) ).
tff(c_3087,plain,
! [X_249] : is_a_theorem(implies(not(not(X_249)),X_249)),
inference(splitRight,[status(thm)],[c_2939]) ).
tff(c_260,plain,
! [Y_4,Z_66,Y_67] :
( is_a_theorem(implies(Y_4,Z_66))
| ~ is_a_theorem(implies(Y_4,Y_67))
| ~ is_a_theorem(implies(Y_67,Z_66)) ),
inference(resolution,[status(thm)],[c_27,c_223]) ).
tff(c_10533,plain,
! [X_520,Z_521] :
( is_a_theorem(implies(not(not(X_520)),Z_521))
| ~ is_a_theorem(implies(X_520,Z_521)) ),
inference(resolution,[status(thm)],[c_3087,c_260]) ).
tff(c_29,plain,
! [X_20,Y_21] : is_a_theorem(implies(implies(not(X_20),not(Y_21)),implies(Y_21,X_20))),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_33,plain,
! [Y_21,X_20] :
( is_a_theorem(implies(Y_21,X_20))
| ~ is_a_theorem(implies(not(X_20),not(Y_21))) ),
inference(resolution,[status(thm)],[c_29,c_2]) ).
tff(c_13349,plain,
! [Y_593,X_594] :
( is_a_theorem(implies(Y_593,not(X_594)))
| ~ is_a_theorem(implies(X_594,not(Y_593))) ),
inference(resolution,[status(thm)],[c_10533,c_33]) ).
tff(c_13515,plain,
! [Y_593] : is_a_theorem(implies(Y_593,not(necessary(not(Y_593))))),
inference(resolution,[status(thm)],[c_12,c_13349]) ).
tff(c_381,plain,
! [X_76,Z_77] :
( is_a_theorem(implies(necessary(X_76),Z_77))
| ~ is_a_theorem(implies(X_76,Z_77)) ),
inference(resolution,[status(thm)],[c_12,c_347]) ).
tff(c_16,plain,
~ is_a_theorem(implies(necessary(a),not(necessary(not(a))))),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_401,plain,
~ is_a_theorem(implies(a,not(necessary(not(a))))),
inference(resolution,[status(thm)],[c_381,c_16]) ).
tff(c_13518,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_13515,c_401]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL039-1 : 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
% 0.10/0.34 % Computer : n011.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sat Sep 5 00:13:13 UTC 2026
% 0.10/0.35 % CPUTime :
% 16.95/6.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.95/6.04
% 16.95/6.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------