%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL218-3 : 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 : n003.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 11:11:32 AM UTC 2026
% Result : Unsatisfiable 113.65s 92.84s
% Output : CNFRefutation 113.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 48 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 143 ( 143 !; 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_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_56,axiom,
! [X,Y] : ( implies(X,Y) = or(not(X),Y) ),
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(implies(or(p,q),q),implies(p,q))),
file(unknown,unknown) ).
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_14,plain,
! [X_14] :
( ~ axiom(X_14)
| theorem(X_14) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
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_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_389,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_515,plain,
! [B_107,B_108,C_109] :
( theorem(or(B_107,or(B_108,C_109)))
| ~ theorem(or(B_107,C_109)) ),
inference(resolution,[status(thm)],[c_72,c_389]) ).
tff(c_530,plain,
! [X_12,B_108,C_109] :
( theorem(implies(X_12,or(B_108,C_109)))
| ~ theorem(or(not(X_12),C_109)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_515]) ).
tff(c_687,plain,
! [X_122,B_123,C_124] :
( theorem(implies(X_122,or(B_123,C_124)))
| ~ theorem(implies(X_122,C_124)) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_530]) ).
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_695,plain,
! [X_125,B_126,C_127] :
( ~ theorem(X_125)
| theorem(or(B_126,C_127))
| ~ theorem(implies(X_125,C_127)) ),
inference(resolution,[status(thm)],[c_687,c_16]) ).
tff(c_993,plain,
! [X_160,B_161,C_162] :
( ~ theorem(X_160)
| theorem(or(B_161,C_162))
| ~ axiom(implies(X_160,C_162)) ),
inference(resolution,[status(thm)],[c_14,c_695]) ).
tff(c_1203,plain,
! [A_184,B_185,B_186] :
( ~ theorem(or(A_184,B_185))
| theorem(or(B_186,or(B_185,A_184))) ),
inference(resolution,[status(thm)],[c_6,c_993]) ).
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_1366,plain,
! [B_207,B_208,A_209] :
( theorem(or(B_207,or(B_208,A_209)))
| ~ theorem(or(A_209,B_207)) ),
inference(resolution,[status(thm)],[c_1203,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_1503,plain,
! [B_219,A_220] :
( theorem(or(B_219,A_220))
| ~ theorem(or(A_220,or(B_219,A_220))) ),
inference(resolution,[status(thm)],[c_1366,c_71]) ).
tff(c_1578,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_1503]) ).
tff(c_1718,plain,
! [X_232,Y_233] :
( theorem(implies(X_232,Y_233))
| ~ theorem(or(Y_233,implies(X_232,Y_233))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1578]) ).
tff(c_2087,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_1718]) ).
tff(c_2170,plain,
! [X_263,C_264] :
( theorem(implies(X_263,C_264))
| ~ axiom(implies(X_263,or(C_264,C_264))) ),
inference(resolution,[status(thm)],[c_14,c_2087]) ).
tff(c_2204,plain,
! [A_2] : theorem(implies(A_2,A_2)),
inference(resolution,[status(thm)],[c_4,c_2170]) ).
tff(c_146,plain,
! [A_40,X_12,C_42] : axiom(implies(or(A_40,or(not(X_12),C_42)),implies(X_12,or(A_40,C_42)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_129]) ).
tff(c_474,plain,
! [A_98,X_99,C_100] : axiom(implies(or(A_98,implies(X_99,C_100)),implies(X_99,or(A_98,C_100)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_146]) ).
tff(c_1853,plain,
! [A_237,X_238,C_239] :
( ~ theorem(or(A_237,implies(X_238,C_239)))
| theorem(implies(X_238,or(A_237,C_239))) ),
inference(resolution,[status(thm)],[c_474,c_43]) ).
tff(c_1924,plain,
! [X_12,X_238,C_239] :
( ~ theorem(implies(X_12,implies(X_238,C_239)))
| theorem(implies(X_238,or(not(X_12),C_239))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1853]) ).
tff(c_2594,plain,
! [X_284,X_285,C_286] :
( ~ theorem(implies(X_284,implies(X_285,C_286)))
| theorem(implies(X_285,implies(X_284,C_286))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1924]) ).
tff(c_2626,plain,
! [X_285,C_286] : theorem(implies(X_285,implies(implies(X_285,C_286),C_286))),
inference(resolution,[status(thm)],[c_2204,c_2594]) ).
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_111,plain,
! [A_36,Y_13,X_12] : axiom(implies(implies(A_36,Y_13),implies(or(not(X_12),A_36),implies(X_12,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_102]) ).
tff(c_383,plain,
! [A_79,Y_80,X_81] : axiom(implies(implies(A_79,Y_80),implies(implies(X_81,A_79),implies(X_81,Y_80)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_111]) ).
tff(c_982,plain,
! [A_157,Y_158,X_159] :
( ~ theorem(implies(A_157,Y_158))
| theorem(implies(implies(X_159,A_157),implies(X_159,Y_158))) ),
inference(resolution,[status(thm)],[c_383,c_43]) ).
tff(c_2817,plain,
! [X_296,A_297,Y_298] :
( ~ theorem(implies(X_296,A_297))
| theorem(implies(X_296,Y_298))
| ~ theorem(implies(A_297,Y_298)) ),
inference(resolution,[status(thm)],[c_982,c_16]) ).
tff(c_8058,plain,
! [X_566,Y_567,A_568] :
( theorem(implies(X_566,Y_567))
| ~ theorem(implies(A_568,Y_567))
| ~ axiom(implies(X_566,A_568)) ),
inference(resolution,[status(thm)],[c_14,c_2817]) ).
tff(c_18323,plain,
! [X_952,Y_953,A_954] :
( theorem(implies(X_952,Y_953))
| ~ axiom(implies(X_952,A_954))
| ~ axiom(implies(A_954,Y_953)) ),
inference(resolution,[status(thm)],[c_14,c_8058]) ).
tff(c_20315,plain,
! [A_990,Y_991,B_992] :
( theorem(implies(A_990,Y_991))
| ~ axiom(implies(or(B_992,A_990),Y_991)) ),
inference(resolution,[status(thm)],[c_4,c_18323]) ).
tff(c_20351,plain,
! [B_993,A_994] : theorem(implies(B_993,or(B_993,A_994))),
inference(resolution,[status(thm)],[c_6,c_20315]) ).
tff(c_992,plain,
! [X_159,A_157,Y_158] :
( ~ theorem(implies(X_159,A_157))
| theorem(implies(X_159,Y_158))
| ~ theorem(implies(A_157,Y_158)) ),
inference(resolution,[status(thm)],[c_982,c_16]) ).
tff(c_49657,plain,
! [B_1774,Y_1775,A_1776] :
( theorem(implies(B_1774,Y_1775))
| ~ theorem(implies(or(B_1774,A_1776),Y_1775)) ),
inference(resolution,[status(thm)],[c_20351,c_992]) ).
tff(c_125084,plain,
! [B_3217,A_3218,C_3219] : theorem(implies(B_3217,implies(implies(or(B_3217,A_3218),C_3219),C_3219))),
inference(resolution,[status(thm)],[c_2626,c_49657]) ).
tff(c_1946,plain,
! [X_12,X_238,C_239] :
( ~ theorem(implies(X_12,implies(X_238,C_239)))
| theorem(implies(X_238,implies(X_12,C_239))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_1924]) ).
tff(c_125354,plain,
! [B_3217,A_3218,C_3219] : theorem(implies(implies(or(B_3217,A_3218),C_3219),implies(B_3217,C_3219))),
inference(resolution,[status(thm)],[c_125084,c_1946]) ).
tff(c_18,plain,
~ theorem(implies(implies(or(p,q),q),implies(p,q))),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_144737,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_125354,c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL218-3 : TPTP v9.3.1. Released v2.3.0.
% 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
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 03:51:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 113.65/92.84 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 113.65/92.86
% 113.65/92.86 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------