%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL041-1 : 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 : n020.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 6.46s 3.24s
% Output : CNFRefutation 6.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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; 2 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 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_35,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file(unknown,unknown) ).
tff(f_39,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z)))),
file(unknown,unknown) ).
tff(f_33,axiom,
! [X,Y] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_43,axiom,
! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(not(X),Y),Y))),
file(unknown,unknown) ).
tff(f_45,axiom,
~ is_a_theorem(implies(implies(a,implies(a,b)),implies(a,b))),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4] : is_a_theorem(implies(X_3,implies(not(X_3),Y_4))),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_106,plain,
! [X_37,Y_38,Z_39] : is_a_theorem(implies(implies(X_37,implies(Y_38,Z_39)),implies(Y_38,implies(X_37,Z_39)))),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_17,plain,
! [Y_19,X_20] :
( is_a_theorem(Y_19)
| ~ is_a_theorem(X_20)
| ~ is_a_theorem(implies(X_20,Y_19)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_24,plain,
! [X_3,Y_4] :
( is_a_theorem(implies(not(X_3),Y_4))
| ~ is_a_theorem(X_3) ),
inference(resolution,[status(thm)],[c_4,c_17]) ).
tff(c_45,plain,
! [X_25,Y_26] : is_a_theorem(implies(implies(X_25,Y_26),implies(implies(not(X_25),Y_26),Y_26))),
inference(cnfTransformation,[status(thm)],[f_43]) ).
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_33]) ).
tff(c_51,plain,
! [X_28,Y_29] :
( is_a_theorem(implies(implies(not(X_28),Y_29),Y_29))
| ~ is_a_theorem(implies(X_28,Y_29)) ),
inference(resolution,[status(thm)],[c_45,c_2]) ).
tff(c_56,plain,
! [Y_30,X_31] :
( is_a_theorem(Y_30)
| ~ is_a_theorem(implies(not(X_31),Y_30))
| ~ is_a_theorem(implies(X_31,Y_30)) ),
inference(resolution,[status(thm)],[c_51,c_2]) ).
tff(c_72,plain,
! [Y_4,X_3] :
( is_a_theorem(Y_4)
| ~ is_a_theorem(implies(X_3,Y_4))
| ~ is_a_theorem(X_3) ),
inference(resolution,[status(thm)],[c_24,c_56]) ).
tff(c_146,plain,
! [Y_45,X_46,Z_47] :
( is_a_theorem(implies(Y_45,implies(X_46,Z_47)))
| ~ is_a_theorem(implies(X_46,implies(Y_45,Z_47))) ),
inference(resolution,[status(thm)],[c_106,c_72]) ).
tff(c_172,plain,
! [X_3,Y_4] : is_a_theorem(implies(not(X_3),implies(X_3,Y_4))),
inference(resolution,[status(thm)],[c_4,c_146]) ).
tff(c_12,plain,
! [X_13,Y_14] : is_a_theorem(implies(implies(X_13,Y_14),implies(implies(not(X_13),Y_14),Y_14))),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_285,plain,
! [X_59,Y_60] : is_a_theorem(implies(implies(not(X_59),Y_60),implies(implies(X_59,Y_60),Y_60))),
inference(resolution,[status(thm)],[c_12,c_146]) ).
tff(c_1602,plain,
! [X_149,Y_150] :
( is_a_theorem(implies(implies(X_149,Y_150),Y_150))
| ~ is_a_theorem(implies(not(X_149),Y_150)) ),
inference(resolution,[status(thm)],[c_285,c_72]) ).
tff(c_14,plain,
~ is_a_theorem(implies(implies(a,implies(a,b)),implies(a,b))),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_1618,plain,
~ is_a_theorem(implies(not(a),implies(a,b))),
inference(resolution,[status(thm)],[c_1602,c_14]) ).
tff(c_1627,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_172,c_1618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL041-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % 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
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 08:36:57 UTC 2026
% 0.11/0.38 % CPUTime :
% 6.46/3.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.46/3.25
% 6.46/3.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------