%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL207-3 : 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 11:11:30 AM UTC 2026
% Result : Unsatisfiable 30.95s 16.07s
% Output : CNFRefutation 30.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 80 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 119 ( 61 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 174 ( 174 !; 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(q,p))),
file(unknown,unknown) ).
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_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_102,plain,
! [A_36,B_37,C_38] : axiom(implies(or(A_36,or(B_37,C_38)),or(B_37,or(A_36,C_38)))),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_112,plain,
! [X_12,B_37,C_38] : axiom(implies(implies(X_12,or(B_37,C_38)),or(B_37,or(not(X_12),C_38)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_102]) ).
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_112]) ).
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_385,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_102,c_43]) ).
tff(c_502,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_385]) ).
tff(c_517,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_502]) ).
tff(c_664,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_517]) ).
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_843,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_664,c_16]) ).
tff(c_914,plain,
! [X_148,B_149,C_150] :
( ~ theorem(X_148)
| theorem(or(B_149,C_150))
| ~ axiom(implies(X_148,C_150)) ),
inference(resolution,[status(thm)],[c_14,c_843]) ).
tff(c_1353,plain,
! [A_196,B_197,B_198] :
( ~ theorem(or(A_196,B_197))
| theorem(or(B_198,or(B_197,A_196))) ),
inference(resolution,[status(thm)],[c_6,c_914]) ).
tff(c_120,plain,
! [A_36,B_37,C_38] :
( ~ theorem(or(A_36,or(B_37,C_38)))
| theorem(or(B_37,or(A_36,C_38))) ),
inference(resolution,[status(thm)],[c_102,c_43]) ).
tff(c_1501,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_1353,c_120]) ).
tff(c_1550,plain,
! [B_220,X_221,Y_222] :
( theorem(or(B_220,implies(X_221,Y_222)))
| ~ theorem(or(Y_222,B_220)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_1501]) ).
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_1872,plain,
! [X_247,Y_248] :
( theorem(implies(X_247,Y_248))
| ~ theorem(or(Y_248,implies(X_247,Y_248))) ),
inference(resolution,[status(thm)],[c_1550,c_71]) ).
tff(c_2119,plain,
! [X_264,C_265] :
( theorem(implies(X_264,C_265))
| ~ theorem(implies(X_264,or(C_265,C_265))) ),
inference(resolution,[status(thm)],[c_317,c_1872]) ).
tff(c_2178,plain,
! [X_266,C_267] :
( theorem(implies(X_266,C_267))
| ~ axiom(implies(X_266,or(C_267,C_267))) ),
inference(resolution,[status(thm)],[c_14,c_2119]) ).
tff(c_2213,plain,
! [A_268] : theorem(implies(A_268,A_268)),
inference(resolution,[status(thm)],[c_4,c_2178]) ).
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_244,plain,
! [Y_58,X_59] : axiom(implies(or(Y_58,not(X_59)),implies(X_59,Y_58))),
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_244]) ).
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_2231,plain,
! [X_67] : theorem(implies(X_67,not(not(X_67)))),
inference(resolution,[status(thm)],[c_2213,c_305]) ).
tff(c_139,plain,
! [A_40,B_41,C_42] : axiom(implies(implies(A_40,B_41),implies(or(C_42,A_40),or(C_42,B_41)))),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_148,plain,
! [A_40,Y_13,X_12] : axiom(implies(implies(A_40,Y_13),implies(or(not(X_12),A_40),implies(X_12,Y_13)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_139]) ).
tff(c_470,plain,
! [A_95,Y_96,X_97] : axiom(implies(implies(A_95,Y_96),implies(implies(X_97,A_95),implies(X_97,Y_96)))),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_148]) ).
tff(c_1861,plain,
! [A_244,Y_245,X_246] :
( ~ theorem(implies(A_244,Y_245))
| theorem(implies(implies(X_246,A_244),implies(X_246,Y_245))) ),
inference(resolution,[status(thm)],[c_470,c_43]) ).
tff(c_2369,plain,
! [X_278,A_279,Y_280] :
( ~ theorem(implies(X_278,A_279))
| theorem(implies(X_278,Y_280))
| ~ theorem(implies(A_279,Y_280)) ),
inference(resolution,[status(thm)],[c_1861,c_16]) ).
tff(c_6112,plain,
! [X_467,Y_468,A_469] :
( theorem(implies(X_467,Y_468))
| ~ theorem(implies(A_469,Y_468))
| ~ axiom(implies(X_467,A_469)) ),
inference(resolution,[status(thm)],[c_14,c_2369]) ).
tff(c_16332,plain,
! [X_868,Y_869,A_870] :
( theorem(implies(X_868,Y_869))
| ~ axiom(implies(X_868,A_870))
| ~ axiom(implies(A_870,Y_869)) ),
inference(resolution,[status(thm)],[c_14,c_6112]) ).
tff(c_20989,plain,
! [A_977,Y_978,B_979] :
( theorem(implies(A_977,Y_978))
| ~ axiom(implies(or(B_979,A_977),Y_978)) ),
inference(resolution,[status(thm)],[c_4,c_16332]) ).
tff(c_21025,plain,
! [B_980,A_981] : theorem(implies(B_980,or(B_980,A_981))),
inference(resolution,[status(thm)],[c_6,c_20989]) ).
tff(c_1871,plain,
! [X_246,A_244,Y_245] :
( ~ theorem(implies(X_246,A_244))
| theorem(implies(X_246,Y_245))
| ~ theorem(implies(A_244,Y_245)) ),
inference(resolution,[status(thm)],[c_1861,c_16]) ).
tff(c_45412,plain,
! [B_1635,Y_1636,A_1637] :
( theorem(implies(B_1635,Y_1636))
| ~ theorem(implies(or(B_1635,A_1637),Y_1636)) ),
inference(resolution,[status(thm)],[c_21025,c_1871]) ).
tff(c_51540,plain,
! [B_1763,A_1764] : theorem(implies(B_1763,not(not(or(B_1763,A_1764))))),
inference(resolution,[status(thm)],[c_2231,c_45412]) ).
tff(c_47,plain,
! [X_12,Y_13] : axiom(implies(implies(X_12,Y_13),or(Y_13,not(X_12)))),
inference(superposition,[status(thm),theory(equality)],[c_12,c_44]) ).
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_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_16375,plain,
! [Y_871,Y_872,X_873] :
( theorem(implies(Y_871,Y_872))
| ~ axiom(implies(implies(X_873,Y_871),Y_872)) ),
inference(resolution,[status(thm)],[c_32,c_16332]) ).
tff(c_16409,plain,
! [Y_13,X_12] : theorem(implies(Y_13,or(Y_13,not(X_12)))),
inference(resolution,[status(thm)],[c_47,c_16375]) ).
tff(c_167,plain,
! [A_45,B_46] :
( ~ theorem(or(A_45,B_46))
| theorem(or(B_46,A_45)) ),
inference(resolution,[status(thm)],[c_6,c_52]) ).
tff(c_171,plain,
! [X_12,Y_13] :
( ~ theorem(implies(X_12,Y_13))
| theorem(or(Y_13,not(X_12))) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_167]) ).
tff(c_544,plain,
! [B_110,C_111] :
( theorem(or(B_110,C_111))
| ~ theorem(or(or(B_110,C_111),C_111)) ),
inference(resolution,[status(thm)],[c_502,c_71]) ).
tff(c_17108,plain,
! [B_890,X_891] :
( theorem(or(B_890,not(X_891)))
| ~ theorem(implies(X_891,or(B_890,not(X_891)))) ),
inference(resolution,[status(thm)],[c_171,c_544]) ).
tff(c_17255,plain,
! [X_892] : theorem(or(X_892,not(X_892))),
inference(resolution,[status(thm)],[c_16409,c_17108]) ).
tff(c_2283,plain,
! [A_272,B_273,C_274] :
( ~ theorem(implies(A_272,B_273))
| theorem(implies(or(C_274,A_272),or(C_274,B_273))) ),
inference(resolution,[status(thm)],[c_139,c_43]) ).
tff(c_2304,plain,
! [C_274,A_272,B_273] :
( ~ theorem(or(C_274,A_272))
| theorem(or(C_274,B_273))
| ~ theorem(implies(A_272,B_273)) ),
inference(resolution,[status(thm)],[c_2283,c_16]) ).
tff(c_23325,plain,
! [X_1043,B_1044] :
( theorem(or(X_1043,B_1044))
| ~ theorem(implies(not(X_1043),B_1044)) ),
inference(resolution,[status(thm)],[c_17255,c_2304]) ).
tff(c_24596,plain,
! [X_1073] : theorem(or(X_1073,not(not(not(X_1073))))),
inference(resolution,[status(thm)],[c_2231,c_23325]) ).
tff(c_252,plain,
! [Y_58,X_59] :
( ~ theorem(or(Y_58,not(X_59)))
| theorem(implies(X_59,Y_58)) ),
inference(resolution,[status(thm)],[c_244,c_43]) ).
tff(c_24621,plain,
! [X_1074] : theorem(implies(not(not(X_1074)),X_1074)),
inference(resolution,[status(thm)],[c_24596,c_252]) ).
tff(c_4855,plain,
! [C_403,A_404,B_405] :
( ~ theorem(or(C_403,A_404))
| theorem(or(C_403,B_405))
| ~ theorem(implies(A_404,B_405)) ),
inference(resolution,[status(thm)],[c_2283,c_16]) ).
tff(c_4962,plain,
! [Y_13,B_405,X_12] :
( theorem(or(Y_13,B_405))
| ~ theorem(implies(not(X_12),B_405))
| ~ theorem(implies(X_12,Y_13)) ),
inference(resolution,[status(thm)],[c_171,c_4855]) ).
tff(c_24699,plain,
! [Y_13,X_1074] :
( theorem(or(Y_13,X_1074))
| ~ theorem(implies(not(X_1074),Y_13)) ),
inference(resolution,[status(thm)],[c_24621,c_4962]) ).
tff(c_51569,plain,
! [X_1074,A_1764] : theorem(or(not(not(or(not(X_1074),A_1764))),X_1074)),
inference(resolution,[status(thm)],[c_51540,c_24699]) ).
tff(c_51693,plain,
! [X_1074,A_1764] : theorem(implies(not(implies(X_1074,A_1764)),X_1074)),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_12,c_51569]) ).
tff(c_866,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_664]) ).
tff(c_18,plain,
~ theorem(implies(not(implies(p,q)),implies(q,p))),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_876,plain,
~ theorem(implies(not(implies(p,q)),p)),
inference(resolution,[status(thm)],[c_866,c_18]) ).
tff(c_51744,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_51693,c_876]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL207-3 : 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 : n003.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 04:19:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 30.95/16.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.95/16.08
% 30.95/16.08 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------