%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL082-1 : 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 : 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 11:11:12 AM UTC 2026
% Result : Unsatisfiable 3.84s 2.59s
% Output : CNFRefutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > implies > #nlpp > 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(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_40,axiom,
! [X,Y,Z,U] : is_a_theorem(implies(implies(implies(X,Y),Z),implies(implies(Z,X),implies(U,X)))),
file(unknown,unknown) ).
tff(f_38,axiom,
! [X,Y] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_42,axiom,
~ is_a_theorem(implies(a,implies(b,a))),
file(unknown,unknown) ).
tff(c_4,plain,
! [X_3,Y_4,Z_5,U_6] : is_a_theorem(implies(implies(implies(X_3,Y_4),Z_5),implies(implies(Z_5,X_3),implies(U_6,X_3)))),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_8,plain,
! [X_9,Y_10,Z_11,U_12] : is_a_theorem(implies(implies(implies(X_9,Y_10),Z_11),implies(implies(Z_11,X_9),implies(U_12,X_9)))),
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_38]) ).
tff(c_13,plain,
! [Z_13,X_14,U_15,Y_16] :
( is_a_theorem(implies(implies(Z_13,X_14),implies(U_15,X_14)))
| ~ is_a_theorem(implies(implies(X_14,Y_16),Z_13)) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_16,plain,
! [X_3,Z_5,U_15,U_6,Y_4] : is_a_theorem(implies(implies(implies(implies(Z_5,X_3),implies(U_6,X_3)),implies(X_3,Y_4)),implies(U_15,implies(X_3,Y_4)))),
inference(resolution,[status(thm)],[c_4,c_13]) ).
tff(c_17,plain,
! [X_18,U_20,U_17,Y_21,Z_19] : is_a_theorem(implies(implies(implies(implies(Z_19,X_18),implies(U_20,X_18)),implies(X_18,Y_21)),implies(U_17,implies(X_18,Y_21)))),
inference(resolution,[status(thm)],[c_4,c_13]) ).
tff(c_12,plain,
! [Z_11,X_9,U_12,Y_10] :
( is_a_theorem(implies(implies(Z_11,X_9),implies(U_12,X_9)))
| ~ is_a_theorem(implies(implies(X_9,Y_10),Z_11)) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_104,plain,
! [U_45,U_46,X_47,Y_44,U_48,Z_49] : is_a_theorem(implies(implies(implies(U_48,implies(X_47,Y_44)),implies(implies(Z_49,X_47),implies(U_45,X_47))),implies(U_46,implies(implies(Z_49,X_47),implies(U_45,X_47))))),
inference(resolution,[status(thm)],[c_17,c_12]) ).
tff(c_472,plain,
! [U_94,Z_98,Y_99,U_97,X_95,U_96] :
( is_a_theorem(implies(U_96,implies(implies(Z_98,X_95),implies(U_97,X_95))))
| ~ is_a_theorem(implies(implies(U_94,implies(X_95,Y_99)),implies(implies(Z_98,X_95),implies(U_97,X_95)))) ),
inference(resolution,[status(thm)],[c_104,c_2]) ).
tff(c_520,plain,
! [U_100,Z_101,Y_102] : is_a_theorem(implies(U_100,implies(implies(Z_101,Y_102),implies(Y_102,Y_102)))),
inference(resolution,[status(thm)],[c_16,c_472]) ).
tff(c_558,plain,
! [Z_101,Y_102,U_100] :
( is_a_theorem(implies(implies(Z_101,Y_102),implies(Y_102,Y_102)))
| ~ is_a_theorem(U_100) ),
inference(resolution,[status(thm)],[c_520,c_2]) ).
tff(c_560,plain,
! [U_100] : ~ is_a_theorem(U_100),
inference(splitLeft,[status(thm)],[c_558]) ).
tff(c_518,plain,
! [U_96,X_3,Y_99,U_6] : is_a_theorem(implies(U_96,implies(implies(implies(X_3,Y_99),X_3),implies(U_6,X_3)))),
inference(resolution,[status(thm)],[c_4,c_472]) ).
tff(c_627,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_560,c_518]) ).
tff(c_629,plain,
! [Z_107,Y_108] : is_a_theorem(implies(implies(Z_107,Y_108),implies(Y_108,Y_108))),
inference(splitRight,[status(thm)],[c_558]) ).
tff(c_786,plain,
! [Y_117,Z_118,U_119] : is_a_theorem(implies(implies(implies(Y_117,Y_117),Z_118),implies(U_119,Z_118))),
inference(resolution,[status(thm)],[c_629,c_12]) ).
tff(c_24,plain,
! [X_18,U_20,U_17,Y_21,Z_19] :
( is_a_theorem(implies(U_17,implies(X_18,Y_21)))
| ~ is_a_theorem(implies(implies(implies(Z_19,X_18),implies(U_20,X_18)),implies(X_18,Y_21))) ),
inference(resolution,[status(thm)],[c_17,c_2]) ).
tff(c_819,plain,
! [U_120,U_121,U_122] : is_a_theorem(implies(U_120,implies(U_121,implies(U_122,U_121)))),
inference(resolution,[status(thm)],[c_786,c_24]) ).
tff(c_856,plain,
! [U_121,U_122,U_120] :
( is_a_theorem(implies(U_121,implies(U_122,U_121)))
| ~ is_a_theorem(U_120) ),
inference(resolution,[status(thm)],[c_819,c_2]) ).
tff(c_857,plain,
! [U_120] : ~ is_a_theorem(U_120),
inference(splitLeft,[status(thm)],[c_856]) ).
tff(c_812,plain,
! [U_17,U_119,U_20] : is_a_theorem(implies(U_17,implies(U_119,implies(U_20,U_119)))),
inference(resolution,[status(thm)],[c_786,c_24]) ).
tff(c_885,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_857,c_812]) ).
tff(c_886,plain,
! [U_121,U_122] : is_a_theorem(implies(U_121,implies(U_122,U_121))),
inference(splitRight,[status(thm)],[c_856]) ).
tff(c_6,plain,
~ is_a_theorem(implies(a,implies(b,a))),
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_891,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_886,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL082-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % 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
% 0.11/0.37 % Computer : n010.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 16:31:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 3.84/2.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.16/2.60
% 4.16/2.60 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------