%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL205-3 : TPTP v9.3.1. Released v2.3.0.
% 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 : n031.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 15.34s 5.45s
% Output : CNFRefutation 15.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 100 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 86 ( 45 ~; 41 |; 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 : 121 ( 121 !; 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_56,axiom,
! [X,Y] : ( implies(X,Y) = or(not(X),Y) ),
file(unknown,unknown) ).
tff(f_48,axiom,
! [A,B] : axiom(implies(A,or(B,A))),
file(unknown,unknown) ).
tff(f_61,axiom,
! [X] :
( theorem(X)
| ~ axiom(X) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file(unknown,unknown) ).
tff(f_69,axiom,
! [X,Y] :
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file(unknown,unknown) ).
tff(f_46,axiom,
! [A] : axiom(implies(or(A,A),A)),
file(unknown,unknown) ).
tff(f_54,axiom,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file(unknown,unknown) ).
tff(f_77,axiom,
~ theorem(implies(not(implies(p,q)),implies(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_56]) ).
tff(c_4,plain,
! [A_2,B_3] : axiom(implies(A_2,or(B_3,A_2))),
inference(cnfTransformation,[status(thm)],[f_48]) ).
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_56]) ).
tff(c_14,plain,
! [X_14] :
( ~ axiom(X_14)
| theorem(X_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_129,plain,
! [A_40,B_41,C_42] : axiom(implies(or(A_40,or(B_41,C_42)),or(B_41,or(A_40,C_42)))),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_139,plain,
! [X_12,B_41,C_42] : axiom(implies(implies(X_12,or(B_41,C_42)),or(B_41,or(not(X_12),C_42)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_129]) ).
tff(c_306,plain,
! [X_68,B_69,C_70] : axiom(implies(implies(X_68,or(B_69,C_70)),or(B_69,implies(X_68,C_70)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_139]) ).
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_69]) ).
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_317,plain,
! [X_68,B_69,C_70] :
( ~ theorem(implies(X_68,or(B_69,C_70)))
| theorem(or(B_69,implies(X_68,C_70))) ),
inference(resolution,[status(thm)],[c_306,c_43]) ).
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_50]) ).
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_393,plain,
! [A_83,B_84,C_85] :
( ~ theorem(or(A_83,or(B_84,C_85)))
| theorem(or(B_84,or(A_83,C_85))) ),
inference(resolution,[status(thm)],[c_129,c_43]) ).
tff(c_506,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_393]) ).
tff(c_521,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_506]) ).
tff(c_668,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_521]) ).
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_69]) ).
tff(c_847,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_668,c_16]) ).
tff(c_921,plain,
! [X_146,B_147,C_148] :
( ~ theorem(X_146)
| theorem(or(B_147,C_148))
| ~ axiom(implies(X_146,C_148)) ),
inference(resolution,[status(thm)],[c_14,c_847]) ).
tff(c_1411,plain,
! [A_205,B_206,B_207] :
( ~ theorem(or(A_205,B_206))
| theorem(or(B_207,or(B_206,A_205))) ),
inference(resolution,[status(thm)],[c_6,c_921]) ).
tff(c_147,plain,
! [A_40,B_41,C_42] :
( ~ theorem(or(A_40,or(B_41,C_42)))
| theorem(or(B_41,or(A_40,C_42))) ),
inference(resolution,[status(thm)],[c_129,c_43]) ).
tff(c_1502,plain,
! [B_216,B_217,A_218] :
( theorem(or(B_216,or(B_217,A_218)))
| ~ theorem(or(A_218,B_216)) ),
inference(resolution,[status(thm)],[c_1411,c_147]) ).
tff(c_2,plain,
! [A_1] : axiom(implies(or(A_1,A_1),A_1)),
inference(cnfTransformation,[status(thm)],[f_46]) ).
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_1746,plain,
! [B_244,A_245] :
( theorem(or(B_244,A_245))
| ~ theorem(or(A_245,or(B_244,A_245))) ),
inference(resolution,[status(thm)],[c_1502,c_71]) ).
tff(c_1829,plain,
! [X_12,Y_13] :
( theorem(or(not(X_12),Y_13))
| ~ theorem(or(Y_13,implies(X_12,Y_13))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1746]) ).
tff(c_1900,plain,
! [X_249,Y_250] :
( theorem(implies(X_249,Y_250))
| ~ theorem(or(Y_250,implies(X_249,Y_250))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1829]) ).
tff(c_2095,plain,
! [X_259,C_260] :
( theorem(implies(X_259,C_260))
| ~ theorem(implies(X_259,or(C_260,C_260))) ),
inference(resolution,[status(thm)],[c_317,c_1900]) ).
tff(c_2154,plain,
! [X_261,C_262] :
( theorem(implies(X_261,C_262))
| ~ axiom(implies(X_261,or(C_262,C_262))) ),
inference(resolution,[status(thm)],[c_14,c_2095]) ).
tff(c_2189,plain,
! [A_263] : theorem(implies(A_263,A_263)),
inference(resolution,[status(thm)],[c_4,c_2154]) ).
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_50]) ).
tff(c_232,plain,
! [X_56,Y_57] : axiom(implies(implies(X_56,Y_57),or(Y_57,not(X_56)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_44]) ).
tff(c_301,plain,
! [X_66,X_67] : axiom(implies(implies(X_66,not(X_67)),implies(X_67,not(X_66)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_232]) ).
tff(c_305,plain,
! [X_66,X_67] :
( ~ theorem(implies(X_66,not(X_67)))
| theorem(implies(X_67,not(X_66))) ),
inference(resolution,[status(thm)],[c_301,c_43]) ).
tff(c_2207,plain,
! [X_67] : theorem(implies(X_67,not(not(X_67)))),
inference(resolution,[status(thm)],[c_2189,c_305]) ).
tff(c_102,plain,
! [A_36,B_37,C_38] : axiom(implies(implies(A_36,B_37),implies(or(C_38,A_36),or(C_38,B_37)))),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_1075,plain,
! [A_161,B_162,C_163] :
( ~ theorem(implies(A_161,B_162))
| theorem(implies(or(C_163,A_161),or(C_163,B_162))) ),
inference(resolution,[status(thm)],[c_102,c_43]) ).
tff(c_3036,plain,
! [C_313,A_314,B_315] :
( ~ theorem(or(C_313,A_314))
| theorem(or(C_313,B_315))
| ~ theorem(implies(A_314,B_315)) ),
inference(resolution,[status(thm)],[c_1075,c_16]) ).
tff(c_8725,plain,
! [C_569,B_570,A_571] :
( theorem(or(C_569,B_570))
| ~ theorem(implies(A_571,B_570))
| ~ axiom(or(C_569,A_571)) ),
inference(resolution,[status(thm)],[c_14,c_3036]) ).
tff(c_8996,plain,
! [C_592,X_593] :
( theorem(or(C_592,not(not(X_593))))
| ~ axiom(or(C_592,X_593)) ),
inference(resolution,[status(thm)],[c_2207,c_8725]) ).
tff(c_196,plain,
! [Y_50,X_51] : axiom(implies(or(Y_50,not(X_51)),implies(X_51,Y_50))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_44]) ).
tff(c_204,plain,
! [Y_50,X_51] :
( ~ theorem(or(Y_50,not(X_51)))
| theorem(implies(X_51,Y_50)) ),
inference(resolution,[status(thm)],[c_196,c_43]) ).
tff(c_9060,plain,
! [X_594,C_595] :
( theorem(implies(not(X_594),C_595))
| ~ axiom(or(C_595,X_594)) ),
inference(resolution,[status(thm)],[c_8996,c_204]) ).
tff(c_870,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_668]) ).
tff(c_18,plain,
~ theorem(implies(not(implies(p,q)),implies(p,not(q)))),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_880,plain,
~ theorem(implies(not(implies(p,q)),not(q))),
inference(resolution,[status(thm)],[c_870,c_18]) ).
tff(c_9125,plain,
~ axiom(or(not(q),implies(p,q))),
inference(resolution,[status(thm)],[c_9060,c_880]) ).
tff(c_9170,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32,c_12,c_9125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL205-3 : TPTP v9.3.1. Released v2.3.0.
% 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 : n031.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 07:56:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 15.34/5.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.34/5.46
% 15.34/5.47 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------