%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL098-1 : 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 : 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 11:11:14 AM UTC 2026
% Result : Unsatisfiable 4.42s 1.92s
% Output : CNFRefutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 7 ( 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 65 ( 65 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > equivalent > #nlpp > falsehood > 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(falsehood,type,
falsehood: $i ).
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,
! [U,Z,X,Y,V] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)),
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(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
file(unknown,unknown) ).
tff(c_4,plain,
! [V_7,Z_4,Y_6,U_3,X_5] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_5,Y_6),equivalent(X_5,Z_4)),U_3),equivalent(equivalent(Y_6,Z_4),U_3)),V_7),V_7)),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_8,plain,
! [U_13,X_14,Y_12,V_10,Z_11] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X_14,Y_12),equivalent(X_14,Z_11)),U_13),equivalent(equivalent(Y_12,Z_11),U_13)),V_10),V_10)),
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,
! [Y_16,V_18,U_15,Z_19,X_17] :
( is_a_theorem(V_18)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_17,Y_16),equivalent(X_17,Z_19)),U_15),equivalent(equivalent(Y_16,Z_19),U_15)),V_18)) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_19,plain,
! [X_20,Z_21,Z_22,Y_23] : is_a_theorem(equivalent(equivalent(equivalent(X_20,Z_21),Z_22),equivalent(equivalent(Y_23,Z_21),equivalent(equivalent(X_20,Y_23),Z_22)))),
inference(resolution,[status(thm)],[c_4,c_13]) ).
tff(c_12,plain,
! [U_13,X_14,Y_12,V_10,Z_11] :
( is_a_theorem(V_10)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_14,Y_12),equivalent(X_14,Z_11)),U_13),equivalent(equivalent(Y_12,Z_11),U_13)),V_10)) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_27,plain,
! [X_14,Z_21,Y_12,Y_23,Z_11] : is_a_theorem(equivalent(equivalent(Y_23,Z_21),equivalent(equivalent(equivalent(equivalent(X_14,Y_12),equivalent(X_14,Z_11)),Y_23),equivalent(equivalent(Y_12,Z_11),Z_21)))),
inference(resolution,[status(thm)],[c_19,c_12]) ).
tff(c_29,plain,
! [Y_24,Z_25,X_26,Z_27] :
( is_a_theorem(equivalent(equivalent(Y_24,Z_25),equivalent(equivalent(X_26,Y_24),Z_27)))
| ~ is_a_theorem(equivalent(equivalent(X_26,Z_25),Z_27)) ),
inference(resolution,[status(thm)],[c_19,c_2]) ).
tff(c_229,plain,
! [U_73,X_75,Z_76,X_72,Y_74,Z_77] :
( is_a_theorem(equivalent(equivalent(X_72,equivalent(equivalent(equivalent(X_75,Y_74),equivalent(X_75,Z_77)),U_73)),Z_76))
| ~ is_a_theorem(equivalent(equivalent(X_72,equivalent(equivalent(Y_74,Z_77),U_73)),Z_76)) ),
inference(resolution,[status(thm)],[c_29,c_12]) ).
tff(c_345,plain,
! [X_93,Z_98,X_94,U_97,Y_95,Z_96] :
( is_a_theorem(Z_98)
| ~ is_a_theorem(equivalent(X_94,equivalent(equivalent(equivalent(X_93,Y_95),equivalent(X_93,Z_96)),U_97)))
| ~ is_a_theorem(equivalent(equivalent(X_94,equivalent(equivalent(Y_95,Z_96),U_97)),Z_98)) ),
inference(resolution,[status(thm)],[c_229,c_2]) ).
tff(c_3517,plain,
! [X_312,Z_315,Z_310,Z_313,Y_311,Z_314] :
( is_a_theorem(Z_313)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X_312,Y_311),Z_314),Z_310),equivalent(equivalent(equivalent(X_312,Z_315),Z_314),equivalent(equivalent(Y_311,Z_315),Z_310))),Z_313)) ),
inference(resolution,[status(thm)],[c_27,c_345]) ).
tff(c_3674,plain,
! [Z_315,Z_4,Y_6,U_3,X_5] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X_5,Y_6),Z_315),U_3),equivalent(equivalent(equivalent(X_5,Z_4),Z_315),equivalent(equivalent(Y_6,Z_4),U_3)))),
inference(resolution,[status(thm)],[c_4,c_3517]) ).
tff(c_6,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_3677,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3674,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL098-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Fri Sep 4 22:21:42 UTC 2026
% 0.02/0.30 % CPUTime :
% 4.42/1.92 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.42/1.93
% 4.42/1.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------