%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL027-1 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n014.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 11:11:06 AM UTC 2026
% Result : Unsatisfiable 3.11s 2.19s
% Output : CNFRefutation 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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; 2 con; 0-2 aty)
% Number of variables : 33 ( 33 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > falsehood > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(falsehood,type,
falsehood: $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_38,axiom,
! [X] : is_a_theorem(implies(implies(implies(X,falsehood),falsehood),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,Z] : is_a_theorem(implies(implies(X,implies(Y,Z)),implies(implies(X,Y),implies(X,Z)))),
file(unknown,unknown) ).
tff(f_42,axiom,
~ is_a_theorem(implies(falsehood,a)),
file(unknown,unknown) ).
tff(c_6,plain,
! [X_5] : is_a_theorem(implies(implies(implies(X_5,falsehood),falsehood),X_5)),
inference(cnfTransformation,[status(thm)],[f_38]) ).
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_12,plain,
! [Y_11,X_12] :
( is_a_theorem(Y_11)
| ~ is_a_theorem(X_12)
| ~ is_a_theorem(implies(X_12,Y_11)) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_16,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_12]) ).
tff(c_46,plain,
! [X_17,Y_18,Z_19] : is_a_theorem(implies(implies(X_17,implies(Y_18,Z_19)),implies(implies(X_17,Y_18),implies(X_17,Z_19)))),
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_51,plain,
! [X_20,Y_21,Z_22] :
( is_a_theorem(implies(implies(X_20,Y_21),implies(X_20,Z_22)))
| ~ is_a_theorem(implies(X_20,implies(Y_21,Z_22))) ),
inference(resolution,[status(thm)],[c_46,c_2]) ).
tff(c_56,plain,
! [X_23,Z_24,Y_25] :
( is_a_theorem(implies(X_23,Z_24))
| ~ is_a_theorem(implies(X_23,Y_25))
| ~ is_a_theorem(implies(X_23,implies(Y_25,Z_24))) ),
inference(resolution,[status(thm)],[c_51,c_2]) ).
tff(c_111,plain,
! [Y_29,Z_30,Y_31] :
( is_a_theorem(implies(Y_29,Z_30))
| ~ is_a_theorem(implies(Y_29,Y_31))
| ~ is_a_theorem(implies(Y_31,Z_30)) ),
inference(resolution,[status(thm)],[c_16,c_56]) ).
tff(c_165,plain,
! [X_38,Z_39,Y_40] :
( is_a_theorem(implies(X_38,Z_39))
| ~ is_a_theorem(implies(implies(Y_40,X_38),Z_39)) ),
inference(resolution,[status(thm)],[c_4,c_111]) ).
tff(c_196,plain,
! [X_5] : is_a_theorem(implies(falsehood,X_5)),
inference(resolution,[status(thm)],[c_6,c_165]) ).
tff(c_10,plain,
~ is_a_theorem(implies(falsehood,a)),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_201,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_196,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL027-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 5 17:12:57 UTC 2026
% 0.10/0.38 % CPUTime :
% 3.11/2.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.27/2.20
% 3.27/2.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------