%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL206-3 : TPTP v9.3.1. Bugfixed v2.4.1.
% 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 : n004.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 11:11:30 AM UTC 2026
% Result : Unsatisfiable 12.78s 5.04s
% Output : CNFRefutation 12.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 84 ( 44 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 115 ( 115 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ theorem > axiom > or > implies > #nlpp > not > q > p
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(theorem,type,
theorem: $i > $o ).
tff(or,type,
or: ( $i * $i ) > $i ).
tff(not,type,
not: $i > $i ).
tff(q,type,
q: $i ).
tff(axiom,type,
axiom: $i > $o ).
tff(p,type,
p: $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_57,axiom,
! [X,Y] : ( implies(X,Y) = or(not(X),Y) ),
file(unknown,unknown) ).
tff(f_49,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X] :
( theorem(X)
| ~ axiom(X) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file(unknown,unknown) ).
tff(f_70,axiom,
! [X,Y] :
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ),
file(unknown,unknown) ).
tff(f_51,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file(unknown,unknown) ).
tff(f_47,axiom,
! [A] : axiom(implies(or(A,A),A)),
file(unknown,unknown) ).
tff(f_55,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file(unknown,unknown) ).
tff(f_78,axiom,
~ theorem(implies(not(implies(p,q)),implies(not(p),not(q)))),
file(unknown,unknown) ).
tff(c_22,plain,
! [X_21,Y_22] : ( or(not(X_21),Y_22) = implies(X_21,Y_22) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_4,plain,
! [A_2,B_3] : axiom(implies(A_2,or(B_3,A_2))),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_32,plain,
! [Y_22,X_21] : axiom(implies(Y_22,implies(X_21,Y_22))),
inference(superposition,[status(thm),theory(equality)],[c_22,c_4]) ).
tff(c_12,plain,
! [X_12,Y_13] : ( or(not(X_12),Y_13) = implies(X_12,Y_13) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_14,plain,
! [X_14] :
( ~ axiom(X_14)
| theorem(X_14) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_134,plain,
! [A_41,B_42,C_43] : axiom(implies(or(A_41,or(B_42,C_43)),or(B_42,or(A_41,C_43)))),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_39,plain,
! [Y_25,X_26] :
( ~ theorem(Y_25)
| ~ theorem(implies(Y_25,X_26))
| theorem(X_26) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_43,plain,
! [Y_25,X_26] :
( ~ theorem(Y_25)
| theorem(X_26)
| ~ axiom(implies(Y_25,X_26)) ),
inference(resolution,[status(thm)],[c_14,c_39]) ).
tff(c_379,plain,
! [A_80,B_81,C_82] :
( ~ theorem(or(A_80,or(B_81,C_82)))
| theorem(or(B_81,or(A_80,C_82))) ),
inference(resolution,[status(thm)],[c_134,c_43]) ).
tff(c_2911,plain,
! [B_342,A_343,C_344] :
( theorem(or(B_342,or(A_343,C_344)))
| ~ axiom(or(A_343,or(B_342,C_344))) ),
inference(resolution,[status(thm)],[c_14,c_379]) ).
tff(c_6,plain,
! [A_4,B_5] : axiom(implies(or(A_4,B_5),or(B_5,A_4))),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_52,plain,
! [Y_30,X_31] :
( ~ theorem(Y_30)
| theorem(X_31)
| ~ axiom(implies(Y_30,X_31)) ),
inference(resolution,[status(thm)],[c_14,c_39]) ).
tff(c_72,plain,
! [A_2,B_3] :
( ~ theorem(A_2)
| theorem(or(B_3,A_2)) ),
inference(resolution,[status(thm)],[c_4,c_52]) ).
tff(c_505,plain,
! [B_104,B_105,C_106] :
( theorem(or(B_104,or(B_105,C_106)))
| ~ theorem(or(B_104,C_106)) ),
inference(resolution,[status(thm)],[c_72,c_379]) ).
tff(c_520,plain,
! [X_12,B_105,C_106] :
( theorem(implies(X_12,or(B_105,C_106)))
| ~ theorem(or(not(X_12),C_106)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_505]) ).
tff(c_667,plain,
! [X_119,B_120,C_121] :
( theorem(implies(X_119,or(B_120,C_121)))
| ~ theorem(implies(X_119,C_121)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_520]) ).
tff(c_16,plain,
! [Y_16,X_15] :
( ~ theorem(Y_16)
| ~ theorem(implies(Y_16,X_15))
| theorem(X_15) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_846,plain,
! [X_136,B_137,C_138] :
( ~ theorem(X_136)
| theorem(or(B_137,C_138))
| ~ theorem(implies(X_136,C_138)) ),
inference(resolution,[status(thm)],[c_667,c_16]) ).
tff(c_966,plain,
! [X_154,B_155,C_156] :
( ~ theorem(X_154)
| theorem(or(B_155,C_156))
| ~ axiom(implies(X_154,C_156)) ),
inference(resolution,[status(thm)],[c_14,c_846]) ).
tff(c_1361,plain,
! [A_198,B_199,B_200] :
( ~ theorem(or(A_198,B_199))
| theorem(or(B_200,or(B_199,A_198))) ),
inference(resolution,[status(thm)],[c_6,c_966]) ).
tff(c_152,plain,
! [A_41,B_42,C_43] :
( ~ theorem(or(A_41,or(B_42,C_43)))
| theorem(or(B_42,or(A_41,C_43))) ),
inference(resolution,[status(thm)],[c_134,c_43]) ).
tff(c_1492,plain,
! [B_213,B_214,A_215] :
( theorem(or(B_213,or(B_214,A_215)))
| ~ theorem(or(A_215,B_213)) ),
inference(resolution,[status(thm)],[c_1361,c_152]) ).
tff(c_2,plain,
! [A_1] : axiom(implies(or(A_1,A_1),A_1)),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_71,plain,
! [A_1] :
( ~ theorem(or(A_1,A_1))
| theorem(A_1) ),
inference(resolution,[status(thm)],[c_2,c_52]) ).
tff(c_1528,plain,
! [B_214,A_215] :
( theorem(or(B_214,A_215))
| ~ theorem(or(A_215,or(B_214,A_215))) ),
inference(resolution,[status(thm)],[c_1492,c_71]) ).
tff(c_2955,plain,
! [A_345,C_346] :
( theorem(or(A_345,C_346))
| ~ axiom(or(A_345,or(C_346,C_346))) ),
inference(resolution,[status(thm)],[c_2911,c_1528]) ).
tff(c_2963,plain,
! [X_12,C_346] :
( theorem(or(not(X_12),C_346))
| ~ axiom(implies(X_12,or(C_346,C_346))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_2955]) ).
tff(c_3049,plain,
! [X_349,C_350] :
( theorem(implies(X_349,C_350))
| ~ axiom(implies(X_349,or(C_350,C_350))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_2963]) ).
tff(c_3084,plain,
! [A_351] : theorem(implies(A_351,A_351)),
inference(resolution,[status(thm)],[c_4,c_3049]) ).
tff(c_44,plain,
! [A_27,B_28] : axiom(implies(or(A_27,B_28),or(B_28,A_27))),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_244,plain,
! [X_58,Y_59] : axiom(implies(implies(X_58,Y_59),or(Y_59,not(X_58)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_44]) ).
tff(c_253,plain,
! [X_60,Y_61] :
( ~ theorem(implies(X_60,Y_61))
| theorem(or(Y_61,not(X_60))) ),
inference(resolution,[status(thm)],[c_244,c_43]) ).
tff(c_263,plain,
! [X_60,X_12] :
( ~ theorem(implies(X_60,not(X_12)))
| theorem(implies(X_12,not(X_60))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_253]) ).
tff(c_3109,plain,
! [X_12] : theorem(implies(X_12,not(not(X_12)))),
inference(resolution,[status(thm)],[c_3084,c_263]) ).
tff(c_112,plain,
! [A_37,B_38,C_39] : axiom(implies(implies(A_37,B_38),implies(or(C_39,A_37),or(C_39,B_38)))),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_121,plain,
! [A_37,Y_13,X_12] : axiom(implies(implies(A_37,Y_13),implies(or(not(X_12),A_37),implies(X_12,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_112]) ).
tff(c_373,plain,
! [A_76,Y_77,X_78] : axiom(implies(implies(A_76,Y_77),implies(implies(X_78,A_76),implies(X_78,Y_77)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_121]) ).
tff(c_2044,plain,
! [A_253,Y_254,X_255] :
( ~ theorem(implies(A_253,Y_254))
| theorem(implies(implies(X_255,A_253),implies(X_255,Y_254))) ),
inference(resolution,[status(thm)],[c_373,c_43]) ).
tff(c_2550,plain,
! [X_306,A_307,Y_308] :
( ~ theorem(implies(X_306,A_307))
| theorem(implies(X_306,Y_308))
| ~ theorem(implies(A_307,Y_308)) ),
inference(resolution,[status(thm)],[c_2044,c_16]) ).
tff(c_7568,plain,
! [X_522,Y_523,A_524] :
( theorem(implies(X_522,Y_523))
| ~ theorem(implies(A_524,Y_523))
| ~ axiom(implies(X_522,A_524)) ),
inference(resolution,[status(thm)],[c_14,c_2550]) ).
tff(c_7755,plain,
! [X_527,X_528] :
( theorem(implies(X_527,not(not(X_528))))
| ~ axiom(implies(X_527,X_528)) ),
inference(resolution,[status(thm)],[c_3109,c_7568]) ).
tff(c_8714,plain,
! [X_589,X_590] :
( theorem(implies(not(X_589),not(X_590)))
| ~ axiom(implies(X_590,X_589)) ),
inference(resolution,[status(thm)],[c_7755,c_263]) ).
tff(c_872,plain,
! [X_139,X_140,Y_141] :
( theorem(implies(X_139,implies(X_140,Y_141)))
| ~ theorem(implies(X_139,Y_141)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_667]) ).
tff(c_18,plain,
~ theorem(implies(not(implies(p,q)),implies(not(p),not(q)))),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_882,plain,
~ theorem(implies(not(implies(p,q)),not(q))),
inference(resolution,[status(thm)],[c_872,c_18]) ).
tff(c_8752,plain,
~ axiom(implies(q,implies(p,q))),
inference(resolution,[status(thm)],[c_8714,c_882]) ).
tff(c_8785,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32,c_8752]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL206-3 : TPTP v9.3.1. Bugfixed v2.4.1.
% 0.00/0.05 % 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
% 0.09/0.36 % Computer : n004.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 20:08:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 12.78/5.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.78/5.06
% 12.78/5.06 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------