%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 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 : n020.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 19.76s 6.75s
% Output : CNFRefutation 20.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 116 ( 116 !; 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_37,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_39,axiom,
! [X] : is_a_theorem(implies(X,X)),
file(unknown,unknown) ).
tff(f_35,axiom,
! [X,Y] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X)
| is_a_theorem(Y) ),
file(unknown,unknown) ).
tff(f_41,axiom,
~ is_a_theorem(implies(implies(implies(a,b),a),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_37]) ).
tff(c_6,plain,
! [X_7] : is_a_theorem(implies(X_7,X_7)),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_15,plain,
! [X_11,Y_12,Z_13,U_14] : is_a_theorem(implies(implies(implies(X_11,Y_12),Z_13),implies(implies(Z_13,X_11),implies(U_14,X_11)))),
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(implies(X_1,Y_2)) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_20,plain,
! [Z_15,X_16,U_17,Y_18] :
( is_a_theorem(implies(implies(Z_15,X_16),implies(U_17,X_16)))
| ~ is_a_theorem(implies(implies(X_16,Y_18),Z_15)) ),
inference(resolution,[status(thm)],[c_15,c_2]) ).
tff(c_28,plain,
! [X_19,Y_20,U_21] : is_a_theorem(implies(implies(implies(X_19,Y_20),X_19),implies(U_21,X_19))),
inference(resolution,[status(thm)],[c_6,c_20]) ).
tff(c_19,plain,
! [Z_13,X_11,U_14,Y_12] :
( is_a_theorem(implies(implies(Z_13,X_11),implies(U_14,X_11)))
| ~ is_a_theorem(implies(implies(X_11,Y_12),Z_13)) ),
inference(resolution,[status(thm)],[c_15,c_2]) ).
tff(c_253,plain,
! [U_61,X_62,Y_63,U_64] : is_a_theorem(implies(implies(implies(U_61,X_62),implies(X_62,Y_63)),implies(U_64,implies(X_62,Y_63)))),
inference(resolution,[status(thm)],[c_28,c_19]) ).
tff(c_718,plain,
! [U_105,X_106,U_108,Y_107,U_104] : is_a_theorem(implies(implies(implies(U_108,implies(X_106,Y_107)),implies(U_104,X_106)),implies(U_105,implies(U_104,X_106)))),
inference(resolution,[status(thm)],[c_253,c_19]) ).
tff(c_2066,plain,
! [Y_203,U_199,X_201,U_200,U_202] :
( is_a_theorem(implies(U_202,implies(U_199,X_201)))
| ~ is_a_theorem(implies(implies(U_200,implies(X_201,Y_203)),implies(U_199,X_201))) ),
inference(resolution,[status(thm)],[c_718,c_2]) ).
tff(c_2151,plain,
! [U_204,U_205,X_206,Y_207] : is_a_theorem(implies(U_204,implies(implies(implies(implies(U_205,X_206),Y_207),X_206),implies(U_205,X_206)))),
inference(resolution,[status(thm)],[c_4,c_2066]) ).
tff(c_2224,plain,
! [U_205,X_206,Y_207,U_204] :
( is_a_theorem(implies(implies(implies(implies(U_205,X_206),Y_207),X_206),implies(U_205,X_206)))
| ~ is_a_theorem(U_204) ),
inference(resolution,[status(thm)],[c_2151,c_2]) ).
tff(c_2225,plain,
! [U_204] : ~ is_a_theorem(U_204),
inference(splitLeft,[status(thm)],[c_2224]) ).
tff(c_2150,plain,
! [U_202,U_6,X_3,Y_203] : is_a_theorem(implies(U_202,implies(implies(implies(implies(U_6,X_3),Y_203),X_3),implies(U_6,X_3)))),
inference(resolution,[status(thm)],[c_4,c_2066]) ).
tff(c_2277,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2225,c_2150]) ).
tff(c_2443,plain,
! [U_213,X_214,Y_215] : is_a_theorem(implies(implies(implies(implies(U_213,X_214),Y_215),X_214),implies(U_213,X_214))),
inference(splitRight,[status(thm)],[c_2224]) ).
tff(c_24738,plain,
! [U_833,X_834,Y_835,U_836] : is_a_theorem(implies(implies(implies(U_833,X_834),implies(implies(U_833,X_834),Y_835)),implies(U_836,implies(implies(U_833,X_834),Y_835)))),
inference(resolution,[status(thm)],[c_2443,c_19]) ).
tff(c_27,plain,
! [X_16,Y_18,U_17] : is_a_theorem(implies(implies(implies(X_16,Y_18),X_16),implies(U_17,X_16))),
inference(resolution,[status(thm)],[c_6,c_20]) ).
tff(c_36,plain,
! [U_22,X_23,Y_24] :
( is_a_theorem(implies(U_22,X_23))
| ~ is_a_theorem(implies(implies(X_23,Y_24),X_23)) ),
inference(resolution,[status(thm)],[c_28,c_2]) ).
tff(c_41,plain,
! [U_25,U_26] : is_a_theorem(implies(U_25,implies(U_26,U_26))),
inference(resolution,[status(thm)],[c_27,c_36]) ).
tff(c_56,plain,
! [U_27,X_28,U_29] : is_a_theorem(implies(implies(implies(U_27,U_27),X_28),implies(U_29,X_28))),
inference(resolution,[status(thm)],[c_41,c_19]) ).
tff(c_69,plain,
! [U_30,X_31,U_32] :
( is_a_theorem(implies(U_30,X_31))
| ~ is_a_theorem(implies(implies(U_32,U_32),X_31)) ),
inference(resolution,[status(thm)],[c_56,c_2]) ).
tff(c_108,plain,
! [U_36,X_37,Y_38,U_39] : is_a_theorem(implies(U_36,implies(implies(implies(X_37,Y_38),X_37),implies(U_39,X_37)))),
inference(resolution,[status(thm)],[c_4,c_69]) ).
tff(c_15380,plain,
! [X_628,X_625,U_626,U_624,Y_627] : is_a_theorem(implies(implies(implies(implies(implies(X_625,Y_627),X_625),implies(U_626,X_625)),X_628),implies(U_624,X_628))),
inference(resolution,[status(thm)],[c_108,c_19]) ).
tff(c_15543,plain,
! [X_628,X_625,U_626,U_624,Y_627] :
( is_a_theorem(implies(U_624,X_628))
| ~ is_a_theorem(implies(implies(implies(implies(X_625,Y_627),X_625),implies(U_626,X_625)),X_628)) ),
inference(resolution,[status(thm)],[c_15380,c_2]) ).
tff(c_24888,plain,
! [U_837,U_838,Y_839,Y_840] : is_a_theorem(implies(U_837,implies(U_838,implies(implies(implies(Y_839,Y_840),Y_839),Y_839)))),
inference(resolution,[status(thm)],[c_24738,c_15543]) ).
tff(c_25138,plain,
! [U_838,Y_839,Y_840,U_837] :
( is_a_theorem(implies(U_838,implies(implies(implies(Y_839,Y_840),Y_839),Y_839)))
| ~ is_a_theorem(U_837) ),
inference(resolution,[status(thm)],[c_24888,c_2]) ).
tff(c_25139,plain,
! [U_837] : ~ is_a_theorem(U_837),
inference(splitLeft,[status(thm)],[c_25138]) ).
tff(c_24842,plain,
! [U_624,U_836,Y_835,Y_627] : is_a_theorem(implies(U_624,implies(U_836,implies(implies(implies(Y_835,Y_627),Y_835),Y_835)))),
inference(resolution,[status(thm)],[c_24738,c_15543]) ).
tff(c_25300,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_25139,c_24842]) ).
tff(c_25790,plain,
! [U_846,Y_847,Y_848] : is_a_theorem(implies(U_846,implies(implies(implies(Y_847,Y_848),Y_847),Y_847))),
inference(splitRight,[status(thm)],[c_25138]) ).
tff(c_26054,plain,
! [Y_847,Y_848,U_846] :
( is_a_theorem(implies(implies(implies(Y_847,Y_848),Y_847),Y_847))
| ~ is_a_theorem(U_846) ),
inference(resolution,[status(thm)],[c_25790,c_2]) ).
tff(c_26055,plain,
! [U_846] : ~ is_a_theorem(U_846),
inference(splitLeft,[status(thm)],[c_26054]) ).
tff(c_25301,plain,
! [U_838,Y_839,Y_840] : is_a_theorem(implies(U_838,implies(implies(implies(Y_839,Y_840),Y_839),Y_839))),
inference(splitRight,[status(thm)],[c_25138]) ).
tff(c_26217,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26055,c_25301]) ).
tff(c_26218,plain,
! [Y_847,Y_848] : is_a_theorem(implies(implies(implies(Y_847,Y_848),Y_847),Y_847)),
inference(splitRight,[status(thm)],[c_26054]) ).
tff(c_8,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_26221,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_26218,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL083-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % 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
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 13:57:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 19.76/6.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.76/6.76
% 19.76/6.76 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------