%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL044-1 : 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 : n031.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 4.26s 2.70s
% Output : CNFRefutation 4.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 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 : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 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_36,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(not(X),Y))),
file(unknown,unknown) ).
tff(f_40,axiom,
! [X,Y,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(Y,implies(X,Z)))),
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_38,axiom,
! [X,Y] : is_a_theorem(implies(X,implies(Y,X))),
file(unknown,unknown) ).
tff(f_44,axiom,
! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(not(X),Y),Y))),
file(unknown,unknown) ).
tff(f_46,axiom,
~ is_a_theorem(implies(a,not(not(a)))),
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_36]) ).
tff(c_46,plain,
! [X_27,Y_28,Z_29] : is_a_theorem(implies(implies(X_27,implies(Y_28,Z_29)),implies(Y_28,implies(X_27,Z_29)))),
inference(cnfTransformation,[status(thm)],[f_40]) ).
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_111,plain,
! [Y_40,X_41,Z_42] :
( is_a_theorem(implies(Y_40,implies(X_41,Z_42)))
| ~ is_a_theorem(implies(X_41,implies(Y_40,Z_42))) ),
inference(resolution,[status(thm)],[c_46,c_2]) ).
tff(c_137,plain,
! [X_3,Y_4] : is_a_theorem(implies(not(X_3),implies(X_3,Y_4))),
inference(resolution,[status(thm)],[c_4,c_111]) ).
tff(c_6,plain,
! [X_5,Y_6] : is_a_theorem(implies(X_5,implies(Y_6,X_5))),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_35,plain,
! [X_23,Y_24] : is_a_theorem(implies(implies(X_23,Y_24),implies(implies(not(X_23),Y_24),Y_24))),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_52,plain,
! [X_31,Y_32] :
( is_a_theorem(implies(implies(not(X_31),Y_32),Y_32))
| ~ is_a_theorem(implies(X_31,Y_32)) ),
inference(resolution,[status(thm)],[c_35,c_2]) ).
tff(c_57,plain,
! [Y_33,X_34] :
( is_a_theorem(Y_33)
| ~ is_a_theorem(implies(not(X_34),Y_33))
| ~ is_a_theorem(implies(X_34,Y_33)) ),
inference(resolution,[status(thm)],[c_52,c_2]) ).
tff(c_699,plain,
! [Y_105,X_106] :
( is_a_theorem(implies(Y_105,not(X_106)))
| ~ is_a_theorem(implies(X_106,implies(Y_105,not(X_106)))) ),
inference(resolution,[status(thm)],[c_6,c_57]) ).
tff(c_760,plain,
! [X_3] : is_a_theorem(implies(X_3,not(not(X_3)))),
inference(resolution,[status(thm)],[c_137,c_699]) ).
tff(c_14,plain,
~ is_a_theorem(implies(a,not(not(a)))),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_769,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_760,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL044-1 : 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
% 0.10/0.36 % Computer : n031.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 05:25:24 UTC 2026
% 0.10/0.36 % CPUTime :
% 4.26/2.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.59/2.70
% 4.59/2.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------