%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL076-2 : 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 : n012.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 11:11:11 AM UTC 2026
% Result : Unsatisfiable 1.29s 1.10s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > not > 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(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_44,axiom,
! [X1] : is_a_theorem(implies(not(not(X1)),X1)),
file(unknown,unknown) ).
tff(f_42,axiom,
! [X,Y] : is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X))),
file(unknown,unknown) ).
tff(f_36,axiom,
! [X,Y] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_46,axiom,
~ is_a_theorem(implies(a,not(not(a)))),
file(unknown,unknown) ).
tff(c_10,plain,
! [X1_10] : is_a_theorem(implies(not(not(X1_10)),X1_10)),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_33,plain,
! [X_18,Y_19] : is_a_theorem(implies(implies(not(X_18),not(Y_19)),implies(Y_19,X_18))),
inference(cnfTransformation,[status(thm)],[f_42]) ).
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_36]) ).
tff(c_39,plain,
! [Y_21,X_22] :
( is_a_theorem(implies(Y_21,X_22))
| ~ is_a_theorem(implies(not(X_22),not(Y_21))) ),
inference(resolution,[status(thm)],[c_33,c_2]) ).
tff(c_48,plain,
! [Y_21] : is_a_theorem(implies(Y_21,not(not(Y_21)))),
inference(resolution,[status(thm)],[c_10,c_39]) ).
tff(c_12,plain,
~ is_a_theorem(implies(a,not(not(a)))),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_56,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_48,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL076-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % 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
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Fri Sep 4 19:41:42 UTC 2026
% 0.02/0.30 % CPUTime :
% 1.29/1.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.29/1.10
% 1.29/1.10 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------