%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL106-1 : 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 : n010.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 11:11:15 AM UTC 2026
% Result : Unsatisfiable 3.86s 2.44s
% Output : CNFRefutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 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; 3 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 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_37,axiom,
! [X,Y,Z] : is_a_theorem(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Z,Y),X)))),
file(unknown,unknown) ).
tff(f_39,axiom,
! [X,Y,Z] : is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),equivalent(Y,Z))),
file(unknown,unknown) ).
tff(f_35,axiom,
! [X,Y] :
( ~ is_a_theorem(equivalent(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_41,axiom,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4,Z_5] : is_a_theorem(equivalent(X_3,equivalent(equivalent(Y_4,Z_5),equivalent(equivalent(Z_5,Y_4),X_3)))),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_6,plain,
! [X_6,Y_7,Z_8] : is_a_theorem(equivalent(equivalent(equivalent(X_6,Y_7),equivalent(X_6,Z_8)),equivalent(Y_7,Z_8))),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_15,plain,
! [X_14,Y_15,Z_16] : is_a_theorem(equivalent(X_14,equivalent(equivalent(Y_15,Z_16),equivalent(equivalent(Z_16,Y_15),X_14)))),
inference(cnfTransformation,[status(thm)],[f_37]) ).
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_35]) ).
tff(c_20,plain,
! [Y_17,Z_18,X_19] :
( is_a_theorem(equivalent(equivalent(Y_17,Z_18),equivalent(equivalent(Z_18,Y_17),X_19)))
| ~ is_a_theorem(X_19) ),
inference(resolution,[status(thm)],[c_15,c_2]) ).
tff(c_32,plain,
! [Z_23,Y_24,X_25] :
( is_a_theorem(equivalent(equivalent(Z_23,Y_24),X_25))
| ~ is_a_theorem(equivalent(Y_24,Z_23))
| ~ is_a_theorem(X_25) ),
inference(resolution,[status(thm)],[c_20,c_2]) ).
tff(c_10,plain,
! [X_11,Y_12,Z_13] : is_a_theorem(equivalent(equivalent(equivalent(X_11,Y_12),equivalent(X_11,Z_13)),equivalent(Y_12,Z_13))),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_14,plain,
! [Y_12,Z_13,X_11] :
( is_a_theorem(equivalent(Y_12,Z_13))
| ~ is_a_theorem(equivalent(equivalent(X_11,Y_12),equivalent(X_11,Z_13))) ),
inference(resolution,[status(thm)],[c_10,c_2]) ).
tff(c_46,plain,
! [Y_26,Z_27,Z_28] :
( is_a_theorem(equivalent(Y_26,Z_27))
| ~ is_a_theorem(equivalent(Y_26,Z_28))
| ~ is_a_theorem(equivalent(Z_28,Z_27)) ),
inference(resolution,[status(thm)],[c_32,c_14]) ).
tff(c_143,plain,
! [X_44,Y_45,Z_46,Z_47] :
( is_a_theorem(equivalent(equivalent(equivalent(X_44,Y_45),equivalent(X_44,Z_46)),Z_47))
| ~ is_a_theorem(equivalent(equivalent(Y_45,Z_46),Z_47)) ),
inference(resolution,[status(thm)],[c_6,c_46]) ).
tff(c_301,plain,
! [X_68,Z_69,Z_70,Y_71] :
( is_a_theorem(equivalent(equivalent(X_68,Z_69),Z_70))
| ~ is_a_theorem(equivalent(equivalent(Y_71,Z_69),equivalent(equivalent(X_68,Y_71),Z_70))) ),
inference(resolution,[status(thm)],[c_143,c_14]) ).
tff(c_325,plain,
! [Y_4,Z_69,Z_5] : is_a_theorem(equivalent(equivalent(Y_4,Z_69),equivalent(equivalent(Z_5,Y_4),equivalent(Z_5,Z_69)))),
inference(resolution,[status(thm)],[c_4,c_301]) ).
tff(c_8,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_328,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_325,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL106-1 : 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
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 5 13:29:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 3.86/2.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.86/2.45
% 3.86/2.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------