%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL117-1 : 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 : 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 11:11:17 AM UTC 2026
% Result : Unsatisfiable 1.45s 1.12s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > equivalent > #nlpp > c > 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(equivalent,type,
equivalent: ( $i * $i ) > $i ).
tff(c,type,
c: $i ).
tff(f_34,axiom,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(Z,X)))),
file(unknown,unknown) ).
tff(f_31,axiom,
! [X,Y] :
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_37,axiom,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(a,c)),equivalent(c,b))),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4,Z_5] : is_a_theorem(equivalent(equivalent(X_3,Y_4),equivalent(equivalent(Z_5,Y_4),equivalent(Z_5,X_3)))),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_8,plain,
! [X_8,Y_9,Z_10] : is_a_theorem(equivalent(equivalent(X_8,Y_9),equivalent(equivalent(Z_10,Y_9),equivalent(Z_10,X_8)))),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_2,plain,
! [Y_2,X_1] :
( is_a_theorem(Y_2)
| ~ is_a_theorem(X_1)
| ~ is_a_theorem(equivalent(X_1,Y_2)) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_13,plain,
! [Z_11,Y_12,X_13] :
( is_a_theorem(equivalent(equivalent(Z_11,Y_12),equivalent(Z_11,X_13)))
| ~ is_a_theorem(equivalent(X_13,Y_12)) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_18,plain,
! [Z_14,X_15,Y_16] :
( is_a_theorem(equivalent(Z_14,X_15))
| ~ is_a_theorem(equivalent(Z_14,Y_16))
| ~ is_a_theorem(equivalent(X_15,Y_16)) ),
inference(resolution,[status(thm)],[c_13,c_2]) ).
tff(c_32,plain,
! [X_21,Y_22,X_23,Z_24] :
( is_a_theorem(equivalent(equivalent(X_21,Y_22),X_23))
| ~ is_a_theorem(equivalent(X_23,equivalent(equivalent(Z_24,Y_22),equivalent(Z_24,X_21)))) ),
inference(resolution,[status(thm)],[c_4,c_18]) ).
tff(c_42,plain,
! [X_25,Y_26] : is_a_theorem(equivalent(equivalent(X_25,Y_26),equivalent(X_25,Y_26))),
inference(resolution,[status(thm)],[c_4,c_32]) ).
tff(c_17,plain,
! [Z_11,X_13,Y_12] :
( is_a_theorem(equivalent(Z_11,X_13))
| ~ is_a_theorem(equivalent(Z_11,Y_12))
| ~ is_a_theorem(equivalent(X_13,Y_12)) ),
inference(resolution,[status(thm)],[c_13,c_2]) ).
tff(c_59,plain,
! [X_27,Y_28,X_29] :
( is_a_theorem(equivalent(equivalent(X_27,Y_28),X_29))
| ~ is_a_theorem(equivalent(X_29,equivalent(X_27,Y_28))) ),
inference(resolution,[status(thm)],[c_42,c_17]) ).
tff(c_69,plain,
! [Z_5,Y_4,X_3] : is_a_theorem(equivalent(equivalent(equivalent(Z_5,Y_4),equivalent(Z_5,X_3)),equivalent(X_3,Y_4))),
inference(resolution,[status(thm)],[c_4,c_59]) ).
tff(c_6,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(a,c)),equivalent(c,b))),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_72,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_69,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL117-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % 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
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Fri Sep 4 21:11:12 UTC 2026
% 0.04/0.30 % CPUTime :
% 1.45/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.45/1.12
% 1.45/1.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------