%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : REL011-2 : TPTP v9.0.0. Released v4.0.0.
% 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 : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 08:29:06 PM UTC 2025
% Result : Unsatisfiable 18.33s 7.15s
% Output : CNFRefutation 18.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 16
% Syntax : Number of formulae : 96 ( 96 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 95 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 123 ( 123 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ meet > join > composition > #nlpp > converse > complement > zero > top > sk3 > sk2 > sk1 > one
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(top,type,
top: $i ).
tff(sk2,type,
sk2: $i ).
tff(sk1,type,
sk1: $i ).
tff(converse,type,
converse: $i > $i ).
tff(join,type,
join: ( $i * $i ) > $i ).
tff(composition,type,
composition: ( $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff(one,type,
one: $i ).
tff(meet,type,
meet: ( $i * $i ) > $i ).
tff(sk3,type,
sk3: $i ).
tff(zero,type,
zero: $i ).
tff(f_48,axiom,
! [A,B] : ( join(A,B) = join(B,A) ),
file(unknown,unknown) ).
tff(f_54,axiom,
! [A,B] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
file(unknown,unknown) ).
tff(f_107,axiom,
meet(composition(sk2,sk1),sk3) != zero,
file(unknown,unknown) ).
tff(f_72,axiom,
! [A] : ( zero = meet(A,complement(A)) ),
file(unknown,unknown) ).
tff(f_70,axiom,
! [A] : ( top = join(A,complement(A)) ),
file(unknown,unknown) ).
tff(f_52,axiom,
! [A,B] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
file(unknown,unknown) ).
tff(f_50,axiom,
! [A,B,C] : ( join(A,join(B,C)) = join(join(A,B),C) ),
file(unknown,unknown) ).
tff(f_58,axiom,
! [A] : ( composition(A,one) = A ),
file(unknown,unknown) ).
tff(f_98,axiom,
! [A,B,C] : ( join(meet(composition(A,B),C),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))) ),
file(unknown,unknown) ).
tff(f_62,axiom,
! [A] : ( converse(converse(A)) = A ),
file(unknown,unknown) ).
tff(f_64,axiom,
! [A,B] : ( converse(join(A,B)) = join(converse(A),converse(B)) ),
file(unknown,unknown) ).
tff(f_66,axiom,
! [A,B] : ( converse(composition(A,B)) = composition(converse(B),converse(A)) ),
file(unknown,unknown) ).
tff(f_68,axiom,
! [A,B] : ( join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ),
file(unknown,unknown) ).
tff(f_60,axiom,
! [A,B,C] : ( composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ),
file(unknown,unknown) ).
tff(f_56,axiom,
! [A,B,C] : ( composition(A,composition(B,C)) = composition(composition(A,B),C) ),
file(unknown,unknown) ).
tff(f_105,axiom,
meet(sk1,composition(converse(sk2),sk3)) = zero,
file(unknown,unknown) ).
tff(c_2,plain,
! [B_2,A_1] : ( join(B_2,A_1) = join(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_115,plain,
! [A_41,B_42] : ( complement(join(complement(A_41),complement(B_42))) = meet(A_41,B_42) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_646,plain,
! [B_62,A_63] : ( complement(join(complement(B_62),complement(A_63))) = meet(A_63,B_62) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_115]) ).
tff(c_8,plain,
! [A_8,B_9] : ( complement(join(complement(A_8),complement(B_9))) = meet(A_8,B_9) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_673,plain,
! [B_62,A_63] : ( meet(B_62,A_63) = meet(A_63,B_62) ),
inference(superposition,[status(thm),theory(equality)],[c_646,c_8]) ).
tff(c_36,plain,
meet(composition(sk2,sk1),sk3) != zero,
inference(cnfTransformation,[status(thm)],[f_107]) ).
tff(c_776,plain,
meet(sk3,composition(sk2,sk1)) != zero,
inference(demodulation,[status(thm),theory(equality)],[c_673,c_36]) ).
tff(c_26,plain,
! [A_25] : ( meet(A_25,complement(A_25)) = zero ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_24,plain,
! [A_24] : ( join(A_24,complement(A_24)) = top ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_149,plain,
! [A_41] : ( meet(A_41,complement(A_41)) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_115]) ).
tff(c_152,plain,
complement(top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_149]) ).
tff(c_6,plain,
! [A_6,B_7] : ( join(complement(join(complement(A_6),complement(B_7))),complement(join(complement(A_6),B_7))) = A_6 ),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_844,plain,
! [A_67,B_68] : ( join(meet(A_67,B_68),complement(join(complement(A_67),B_68))) = A_67 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_913,plain,
! [A_25] : ( join(zero,complement(join(complement(A_25),complement(A_25)))) = A_25 ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_844]) ).
tff(c_921,plain,
! [A_25] : ( join(zero,meet(A_25,A_25)) = A_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_913]) ).
tff(c_910,plain,
! [A_67] : ( join(meet(A_67,complement(complement(A_67))),complement(top)) = A_67 ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_844]) ).
tff(c_920,plain,
! [A_67] : ( join(zero,meet(A_67,complement(complement(A_67)))) = A_67 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_152,c_910]) ).
tff(c_162,plain,
join(top,zero) = top,
inference(superposition,[status(thm),theory(equality)],[c_152,c_24]) ).
tff(c_360,plain,
! [A_50,B_51,C_52] : ( join(join(A_50,B_51),C_52) = join(A_50,join(B_51,C_52)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_414,plain,
! [C_53] : ( join(top,join(zero,C_53)) = join(top,C_53) ),
inference(superposition,[status(thm),theory(equality)],[c_162,c_360]) ).
tff(c_435,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm),theory(equality)],[c_24,c_414]) ).
tff(c_159,plain,
! [A_8] : ( complement(join(complement(A_8),zero)) = meet(A_8,top) ),
inference(superposition,[status(thm),theory(equality)],[c_152,c_8]) ).
tff(c_193,plain,
! [A_45] : ( complement(join(zero,complement(A_45))) = meet(A_45,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_159]) ).
tff(c_227,plain,
meet(zero,top) = complement(top),
inference(superposition,[status(thm),theory(equality)],[c_24,c_193]) ).
tff(c_230,plain,
meet(zero,top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_152,c_227]) ).
tff(c_880,plain,
join(zero,complement(join(complement(zero),top))) = zero,
inference(superposition,[status(thm),theory(equality)],[c_230,c_844]) ).
tff(c_918,plain,
join(zero,complement(join(top,top))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_435,c_2,c_880]) ).
tff(c_388,plain,
! [C_52] : ( join(top,join(zero,C_52)) = join(top,C_52) ),
inference(superposition,[status(thm),theory(equality)],[c_162,c_360]) ).
tff(c_1020,plain,
join(top,complement(join(top,top))) = join(top,zero),
inference(superposition,[status(thm),theory(equality)],[c_918,c_388]) ).
tff(c_1032,plain,
join(top,complement(join(top,top))) = top,
inference(demodulation,[status(thm),theory(equality)],[c_162,c_1020]) ).
tff(c_168,plain,
! [A_8] : ( complement(join(zero,complement(A_8))) = meet(A_8,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_159]) ).
tff(c_1029,plain,
meet(join(top,top),top) = complement(zero),
inference(superposition,[status(thm),theory(equality)],[c_918,c_168]) ).
tff(c_37,plain,
! [A_6,B_7] : ( join(meet(A_6,B_7),complement(join(complement(A_6),B_7))) = A_6 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_1052,plain,
join(complement(zero),complement(join(complement(join(top,top)),top))) = join(top,top),
inference(superposition,[status(thm),theory(equality)],[c_1029,c_37]) ).
tff(c_1067,plain,
join(top,top) = top,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_152,c_2,c_1032,c_2,c_1052]) ).
tff(c_1155,plain,
join(zero,complement(top)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_1067,c_918]) ).
tff(c_1158,plain,
join(zero,zero) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_152,c_1155]) ).
tff(c_4,plain,
! [A_3,B_4,C_5] : ( join(join(A_3,B_4),C_5) = join(A_3,join(B_4,C_5)) ),
inference(cnfTransformation,[status(thm)],[f_50]) ).
tff(c_1509,plain,
! [C_85] : ( join(zero,join(zero,C_85)) = join(zero,C_85) ),
inference(superposition,[status(thm),theory(equality)],[c_1158,c_4]) ).
tff(c_1536,plain,
! [A_67] : ( join(zero,meet(A_67,complement(complement(A_67)))) = join(zero,A_67) ),
inference(superposition,[status(thm),theory(equality)],[c_920,c_1509]) ).
tff(c_1578,plain,
! [A_86] : ( join(zero,A_86) = A_86 ),
inference(demodulation,[status(thm),theory(equality)],[c_920,c_1536]) ).
tff(c_1619,plain,
! [A_25] : ( meet(A_25,A_25) = A_25 ),
inference(superposition,[status(thm),theory(equality)],[c_921,c_1578]) ).
tff(c_12,plain,
! [A_13] : ( composition(A_13,one) = A_13 ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_28,plain,
! [A_26,B_27,C_28] : ( join(meet(composition(A_26,B_27),C_28),composition(meet(A_26,composition(C_28,converse(B_27))),meet(B_27,composition(converse(A_26),C_28)))) = composition(meet(A_26,composition(C_28,converse(B_27))),meet(B_27,composition(converse(A_26),C_28))) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_3375,plain,
! [A_112,B_113] : ( join(A_112,join(B_113,complement(join(A_112,B_113)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_360]) ).
tff(c_3426,plain,
! [A_26,B_27,C_28] : ( join(meet(composition(A_26,B_27),C_28),join(composition(meet(A_26,composition(C_28,converse(B_27))),meet(B_27,composition(converse(A_26),C_28))),complement(composition(meet(A_26,composition(C_28,converse(B_27))),meet(B_27,composition(converse(A_26),C_28)))))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_28,c_3375]) ).
tff(c_3496,plain,
! [A_114,B_115,C_116] : ( join(top,meet(composition(A_114,B_115),C_116)) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24,c_3426]) ).
tff(c_3545,plain,
! [A_117,C_118] : ( join(top,meet(A_117,C_118)) = top ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_3496]) ).
tff(c_3586,plain,
! [A_119] : ( join(top,A_119) = top ),
inference(superposition,[status(thm),theory(equality)],[c_1619,c_3545]) ).
tff(c_16,plain,
! [A_17] : ( converse(converse(A_17)) = A_17 ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_254,plain,
! [A_46,B_47] : ( join(converse(A_46),converse(B_47)) = converse(join(A_46,B_47)) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_278,plain,
! [A_46,A_17] : ( converse(join(A_46,converse(A_17))) = join(converse(A_46),A_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_254]) ).
tff(c_4363,plain,
! [A_129] : ( join(converse(top),A_129) = converse(top) ),
inference(superposition,[status(thm),theory(equality)],[c_3586,c_278]) ).
tff(c_4422,plain,
converse(top) = top,
inference(superposition,[status(thm),theory(equality)],[c_4363,c_24]) ).
tff(c_1566,plain,
! [A_67] : ( join(zero,A_67) = A_67 ),
inference(demodulation,[status(thm),theory(equality)],[c_920,c_1536]) ).
tff(c_170,plain,
! [B_43,A_44] : ( composition(converse(B_43),converse(A_44)) = converse(composition(A_44,B_43)) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_179,plain,
! [A_44,A_17] : ( converse(composition(A_44,converse(A_17))) = composition(A_17,converse(A_44)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_170]) ).
tff(c_21856,plain,
! [A_260] : ( composition(top,converse(A_260)) = converse(composition(A_260,top)) ),
inference(superposition,[status(thm),theory(equality)],[c_4422,c_179]) ).
tff(c_21916,plain,
converse(composition(top,top)) = composition(top,top),
inference(superposition,[status(thm),theory(equality)],[c_4422,c_21856]) ).
tff(c_20,plain,
! [B_21,A_20] : ( composition(converse(B_21),converse(A_20)) = converse(composition(A_20,B_21)) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_585,plain,
! [A_60,B_61] : ( join(composition(converse(A_60),complement(composition(A_60,B_61))),complement(B_61)) = complement(B_61) ),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_618,plain,
! [B_21,A_20] : ( join(composition(converse(converse(B_21)),complement(converse(composition(A_20,B_21)))),complement(converse(A_20))) = complement(converse(A_20)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_585]) ).
tff(c_26908,plain,
! [A_283,B_284] : ( join(complement(converse(A_283)),composition(B_284,complement(converse(composition(A_283,B_284))))) = complement(converse(A_283)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16,c_618]) ).
tff(c_27013,plain,
join(complement(converse(top)),composition(top,complement(composition(top,top)))) = complement(converse(top)),
inference(superposition,[status(thm),theory(equality)],[c_21916,c_26908]) ).
tff(c_27129,plain,
composition(top,complement(composition(top,top))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_152,c_4422,c_1566,c_152,c_4422,c_27013]) ).
tff(c_3564,plain,
! [A_25] : ( join(top,A_25) = top ),
inference(superposition,[status(thm),theory(equality)],[c_1619,c_3545]) ).
tff(c_14,plain,
! [A_14,C_16,B_15] : ( join(composition(A_14,C_16),composition(B_15,C_16)) = composition(join(A_14,B_15),C_16) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_27226,plain,
! [B_15] : ( join(zero,composition(B_15,complement(composition(top,top)))) = composition(join(top,B_15),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_27129,c_14]) ).
tff(c_27245,plain,
! [B_15] : ( composition(B_15,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_27129,c_3564,c_1566,c_27226]) ).
tff(c_27777,plain,
! [B_287] : ( composition(B_287,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_27129,c_3564,c_1566,c_27226]) ).
tff(c_10,plain,
! [A_10,B_11,C_12] : ( composition(composition(A_10,B_11),C_12) = composition(A_10,composition(B_11,C_12)) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_27855,plain,
! [A_10,B_11] : ( composition(A_10,composition(B_11,complement(composition(top,top)))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_27777,c_10]) ).
tff(c_27886,plain,
! [A_10] : ( composition(A_10,zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_27245,c_27855]) ).
tff(c_34,plain,
meet(sk1,composition(converse(sk2),sk3)) = zero,
inference(cnfTransformation,[status(thm)],[f_105]) ).
tff(c_1317,plain,
! [A_80,B_81,C_82] : ( join(meet(composition(A_80,B_81),C_82),composition(meet(A_80,composition(C_82,converse(B_81))),meet(B_81,composition(converse(A_80),C_82)))) = composition(meet(A_80,composition(C_82,converse(B_81))),meet(B_81,composition(converse(A_80),C_82))) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_1401,plain,
! [A_17,B_81,C_82] : ( join(meet(composition(converse(A_17),B_81),C_82),composition(meet(converse(A_17),composition(C_82,converse(B_81))),meet(B_81,composition(A_17,C_82)))) = composition(meet(converse(A_17),composition(C_82,converse(B_81))),meet(B_81,composition(converse(converse(A_17)),C_82))) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_1317]) ).
tff(c_39579,plain,
! [A_357,B_358,C_359] : ( join(meet(composition(converse(A_357),B_358),C_359),composition(meet(converse(A_357),composition(C_359,converse(B_358))),meet(B_358,composition(A_357,C_359)))) = composition(meet(converse(A_357),composition(C_359,converse(B_358))),meet(B_358,composition(A_357,C_359))) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_1401]) ).
tff(c_39992,plain,
join(meet(composition(converse(converse(sk2)),sk1),sk3),composition(meet(converse(converse(sk2)),composition(sk3,converse(sk1))),zero)) = composition(meet(converse(converse(sk2)),composition(sk3,converse(sk1))),meet(sk1,composition(converse(sk2),sk3))),
inference(superposition,[status(thm),theory(equality)],[c_34,c_39579]) ).
tff(c_40104,plain,
meet(sk3,composition(sk2,sk1)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_27886,c_1566,c_2,c_27886,c_673,c_34,c_16,c_16,c_16,c_39992]) ).
tff(c_40106,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_776,c_40104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL011-2 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.13 % 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
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 8 17:45:32 EDT 2025
% 0.13/0.34 % CPUTime :
% 18.33/7.15 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.33/7.17
% 18.33/7.17 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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