%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL130-1 : 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 : n008.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 11:11:18 AM UTC 2026
% Result : Unsatisfiable 5.69s 2.94s
% Output : CNFRefutation 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 6 ( 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > equivalent > #nlpp > e > 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(e,type,
e: $i ).
tff(c,type,
c: $i ).
tff(f_37,axiom,
! [X,Y,Z,U] : is_a_theorem(equivalent(equivalent(X,equivalent(equivalent(Y,Z),equivalent(equivalent(Y,U),equivalent(Z,U)))),X)),
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_39,axiom,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4,Z_5,U_6] : is_a_theorem(equivalent(equivalent(X_3,equivalent(equivalent(Y_4,Z_5),equivalent(equivalent(Y_4,U_6),equivalent(Z_5,U_6)))),X_3)),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_8,plain,
! [X_9,Y_10,Z_11,U_12] : is_a_theorem(equivalent(equivalent(X_9,equivalent(equivalent(Y_10,Z_11),equivalent(equivalent(Y_10,U_12),equivalent(Z_11,U_12)))),X_9)),
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_13,plain,
! [X_13,Y_14,Z_15,U_16] :
( is_a_theorem(X_13)
| ~ is_a_theorem(equivalent(X_13,equivalent(equivalent(Y_14,Z_15),equivalent(equivalent(Y_14,U_16),equivalent(Z_15,U_16))))) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_19,plain,
! [U_19,Z_17,Z_20,Y_22,U_21,Y_18] : is_a_theorem(equivalent(equivalent(equivalent(Y_18,Z_17),equivalent(equivalent(Y_18,U_19),equivalent(Z_17,U_19))),equivalent(equivalent(Y_22,Z_20),equivalent(equivalent(Y_22,U_21),equivalent(Z_20,U_21))))),
inference(resolution,[status(thm)],[c_4,c_13]) ).
tff(c_12,plain,
! [X_9,Y_10,Z_11,U_12] :
( is_a_theorem(X_9)
| ~ is_a_theorem(equivalent(X_9,equivalent(equivalent(Y_10,Z_11),equivalent(equivalent(Y_10,U_12),equivalent(Z_11,U_12))))) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_28,plain,
! [Y_23,Z_24,U_25] : is_a_theorem(equivalent(equivalent(Y_23,Z_24),equivalent(equivalent(Y_23,U_25),equivalent(Z_24,U_25)))),
inference(resolution,[status(thm)],[c_19,c_12]) ).
tff(c_33,plain,
! [Y_26,U_27,Z_28] :
( is_a_theorem(equivalent(equivalent(Y_26,U_27),equivalent(Z_28,U_27)))
| ~ is_a_theorem(equivalent(Y_26,Z_28)) ),
inference(resolution,[status(thm)],[c_28,c_2]) ).
tff(c_43,plain,
! [Z_29,U_30,Y_31] :
( is_a_theorem(equivalent(Z_29,U_30))
| ~ is_a_theorem(equivalent(Y_31,U_30))
| ~ is_a_theorem(equivalent(Y_31,Z_29)) ),
inference(resolution,[status(thm)],[c_33,c_2]) ).
tff(c_420,plain,
! [Z_87,U_90,Z_89,X_88,Y_91] :
( is_a_theorem(equivalent(Z_87,X_88))
| ~ is_a_theorem(equivalent(equivalent(X_88,equivalent(equivalent(Y_91,Z_89),equivalent(equivalent(Y_91,U_90),equivalent(Z_89,U_90)))),Z_87)) ),
inference(resolution,[status(thm)],[c_4,c_43]) ).
tff(c_470,plain,
! [X_92] : is_a_theorem(equivalent(X_92,X_92)),
inference(resolution,[status(thm)],[c_4,c_420]) ).
tff(c_42,plain,
! [Z_28,U_27,Y_26] :
( is_a_theorem(equivalent(Z_28,U_27))
| ~ is_a_theorem(equivalent(Y_26,U_27))
| ~ is_a_theorem(equivalent(Y_26,Z_28)) ),
inference(resolution,[status(thm)],[c_33,c_2]) ).
tff(c_520,plain,
! [Z_93,X_94] :
( is_a_theorem(equivalent(Z_93,X_94))
| ~ is_a_theorem(equivalent(X_94,Z_93)) ),
inference(resolution,[status(thm)],[c_470,c_42]) ).
tff(c_560,plain,
! [X_3,Y_4,Z_5,U_6] : is_a_theorem(equivalent(X_3,equivalent(X_3,equivalent(equivalent(Y_4,Z_5),equivalent(equivalent(Y_4,U_6),equivalent(Z_5,U_6)))))),
inference(resolution,[status(thm)],[c_4,c_520]) ).
tff(c_6,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_1449,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_560,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL130-1 : 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
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 18:00:53 UTC 2026
% 0.11/0.37 % CPUTime :
% 5.69/2.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.69/2.95
% 5.69/2.95 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------