TSTP Solution File: REL044-2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : REL044-2 : TPTP v8.1.2. 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 : n022.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 : Tue Aug 22 10:54:37 EDT 2023
% Result : Unsatisfiable 132.50s 110.17s
% Output : CNFRefutation 132.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 27
% Syntax : Number of formulae : 175 ( 164 unt; 11 typ; 0 def)
% Number of atoms : 164 ( 163 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 : 8 ( 5 >; 3 *; 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 : 242 (; 242 !; 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_47,axiom,
! [A,B] : ( join(A,B) = join(B,A) ),
file(unknown,unknown) ).
tff(f_106,axiom,
join(composition(sk3,converse(sk2)),sk1) != sk1,
file(unknown,unknown) ).
tff(f_71,axiom,
! [A] : ( zero = meet(A,complement(A)) ),
file(unknown,unknown) ).
tff(f_69,axiom,
! [A] : ( top = join(A,complement(A)) ),
file(unknown,unknown) ).
tff(f_53,axiom,
! [A,B] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [A] : ( composition(A,one) = A ),
file(unknown,unknown) ).
tff(f_97,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_49,axiom,
! [A,B,C] : ( join(A,join(B,C)) = join(join(A,B),C) ),
file(unknown,unknown) ).
tff(f_51,axiom,
! [A,B] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
file(unknown,unknown) ).
tff(f_61,axiom,
! [A] : ( converse(converse(A)) = A ),
file(unknown,unknown) ).
tff(f_65,axiom,
! [A,B] : ( converse(composition(A,B)) = composition(converse(B),converse(A)) ),
file(unknown,unknown) ).
tff(f_55,axiom,
! [A,B,C] : ( composition(A,composition(B,C)) = composition(composition(A,B),C) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [A,B] : ( join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ),
file(unknown,unknown) ).
tff(f_63,axiom,
! [A,B] : ( converse(join(A,B)) = join(converse(A),converse(B)) ),
file(unknown,unknown) ).
tff(f_59,axiom,
! [A,B,C] : ( composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ),
file(unknown,unknown) ).
tff(f_104,axiom,
join(composition(complement(sk1),sk2),complement(sk3)) = complement(sk3),
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_47]) ).
tff(c_36,plain,
join(composition(sk3,converse(sk2)),sk1) != sk1,
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_38,plain,
join(sk1,composition(sk3,converse(sk2))) != sk1,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_36]) ).
tff(c_26,plain,
! [A_25] : ( meet(A_25,complement(A_25)) = zero ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_24,plain,
! [A_24] : ( join(A_24,complement(A_24)) = top ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_112,plain,
! [A_41,B_42] : ( complement(join(complement(A_41),complement(B_42))) = meet(A_41,B_42) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_146,plain,
! [A_41] : ( meet(A_41,complement(A_41)) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_112]) ).
tff(c_149,plain,
complement(top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_146]) ).
tff(c_12,plain,
! [A_13] : ( composition(A_13,one) = A_13 ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_1790,plain,
! [A_89,B_90,C_91] : ( join(meet(composition(A_89,B_90),C_91),composition(meet(A_89,composition(C_91,converse(B_90))),meet(B_90,composition(converse(A_89),C_91)))) = composition(meet(A_89,composition(C_91,converse(B_90))),meet(B_90,composition(converse(A_89),C_91))) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_762,plain,
! [A_63,B_64,C_65] : ( join(join(A_63,B_64),C_65) = join(A_63,join(B_64,C_65)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_844,plain,
! [A_63,B_64] : ( join(A_63,join(B_64,complement(join(A_63,B_64)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_762]) ).
tff(c_1796,plain,
! [A_89,B_90,C_91] : ( join(meet(composition(A_89,B_90),C_91),join(composition(meet(A_89,composition(C_91,converse(B_90))),meet(B_90,composition(converse(A_89),C_91))),complement(composition(meet(A_89,composition(C_91,converse(B_90))),meet(B_90,composition(converse(A_89),C_91)))))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_1790,c_844]) ).
tff(c_2099,plain,
! [A_95,B_96,C_97] : ( join(top,meet(composition(A_95,B_96),C_97)) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24,c_1796]) ).
tff(c_2136,plain,
! [A_13,C_97] : ( join(top,meet(A_13,C_97)) = top ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_2099]) ).
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_53]) ).
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_51]) ).
tff(c_987,plain,
! [A_70,B_71] : ( join(meet(A_70,B_71),complement(join(complement(A_70),B_71))) = A_70 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_1057,plain,
! [A_25] : ( join(zero,complement(join(complement(A_25),complement(A_25)))) = A_25 ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_987]) ).
tff(c_1066,plain,
! [A_72] : ( join(zero,meet(A_72,A_72)) = A_72 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1057]) ).
tff(c_159,plain,
join(top,zero) = top,
inference(superposition,[status(thm),theory(equality)],[c_149,c_24]) ).
tff(c_823,plain,
! [C_65] : ( join(top,join(zero,C_65)) = join(top,C_65) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_762]) ).
tff(c_1072,plain,
! [A_72] : ( join(top,meet(A_72,A_72)) = join(top,A_72) ),
inference(superposition,[status(thm),theory(equality)],[c_1066,c_823]) ).
tff(c_2144,plain,
! [A_72] : ( join(top,A_72) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_2136,c_1072]) ).
tff(c_16,plain,
! [A_17] : ( converse(converse(A_17)) = A_17 ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_362,plain,
! [B_48,A_49] : ( composition(converse(B_48),converse(A_49)) = converse(composition(A_49,B_48)) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_2371,plain,
! [A_102,B_103] : ( converse(composition(converse(A_102),B_103)) = composition(converse(B_103),A_102) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_362]) ).
tff(c_2453,plain,
! [A_102] : ( composition(converse(one),A_102) = converse(converse(A_102)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_2371]) ).
tff(c_2473,plain,
! [A_102] : ( composition(converse(one),A_102) = A_102 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_2453]) ).
tff(c_2479,plain,
! [A_104] : ( composition(converse(one),A_104) = A_104 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_2453]) ).
tff(c_578,plain,
! [A_56,B_57,C_58] : ( composition(composition(A_56,B_57),C_58) = composition(A_56,composition(B_57,C_58)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_600,plain,
! [A_13,C_58] : ( composition(A_13,composition(one,C_58)) = composition(A_13,C_58) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_578]) ).
tff(c_2533,plain,
! [C_58] : ( composition(converse(one),C_58) = composition(one,C_58) ),
inference(superposition,[status(thm),theory(equality)],[c_2479,c_600]) ).
tff(c_2571,plain,
! [C_58] : ( composition(one,C_58) = C_58 ),
inference(demodulation,[status(thm),theory(equality)],[c_2473,c_2533]) ).
tff(c_2544,plain,
converse(one) = one,
inference(superposition,[status(thm),theory(equality)],[c_2479,c_12]) ).
tff(c_2635,plain,
! [C_105] : ( composition(one,C_105) = C_105 ),
inference(demodulation,[status(thm),theory(equality)],[c_2473,c_2533]) ).
tff(c_22,plain,
! [A_22,B_23] : ( join(composition(converse(A_22),complement(composition(A_22,B_23))),complement(B_23)) = complement(B_23) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_2666,plain,
! [C_105] : ( join(composition(converse(one),complement(C_105)),complement(C_105)) = complement(C_105) ),
inference(superposition,[status(thm),theory(equality)],[c_2635,c_22]) ).
tff(c_3997,plain,
! [C_121] : ( join(complement(C_121),complement(C_121)) = complement(C_121) ),
inference(demodulation,[status(thm),theory(equality)],[c_2571,c_2,c_2544,c_2666]) ).
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_4009,plain,
! [C_121] : ( join(meet(C_121,complement(C_121)),complement(complement(C_121))) = C_121 ),
inference(superposition,[status(thm),theory(equality)],[c_3997,c_37]) ).
tff(c_4075,plain,
! [C_122] : ( join(zero,complement(complement(C_122))) = C_122 ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_4009]) ).
tff(c_156,plain,
! [A_8] : ( complement(join(complement(A_8),zero)) = meet(A_8,top) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_8]) ).
tff(c_165,plain,
! [A_8] : ( complement(join(zero,complement(A_8))) = meet(A_8,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_156]) ).
tff(c_4400,plain,
! [C_126] : ( meet(complement(C_126),top) = complement(C_126) ),
inference(superposition,[status(thm),theory(equality)],[c_4075,c_165]) ).
tff(c_4412,plain,
! [C_126] : ( join(complement(C_126),complement(join(complement(complement(C_126)),top))) = complement(C_126) ),
inference(superposition,[status(thm),theory(equality)],[c_4400,c_37]) ).
tff(c_4481,plain,
! [C_127] : ( join(zero,complement(C_127)) = complement(C_127) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_149,c_2144,c_2,c_4412]) ).
tff(c_4061,plain,
! [C_121] : ( join(zero,complement(complement(C_121))) = C_121 ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_4009]) ).
tff(c_4487,plain,
! [C_121] : ( complement(complement(C_121)) = C_121 ),
inference(superposition,[status(thm),theory(equality)],[c_4481,c_4061]) ).
tff(c_142,plain,
! [B_42,A_41] : ( complement(join(complement(B_42),complement(A_41))) = meet(A_41,B_42) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_112]) ).
tff(c_4129,plain,
! [C_123] : ( meet(C_123,C_123) = complement(complement(C_123)) ),
inference(superposition,[status(thm),theory(equality)],[c_3997,c_142]) ).
tff(c_1065,plain,
! [A_25] : ( join(zero,meet(A_25,A_25)) = A_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1057]) ).
tff(c_306,plain,
! [A_45,B_46] : ( join(converse(A_45),converse(B_46)) = converse(join(A_45,B_46)) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_2700,plain,
! [B_106,A_107] : ( join(converse(B_106),converse(A_107)) = converse(join(A_107,B_106)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_306]) ).
tff(c_18,plain,
! [A_18,B_19] : ( join(converse(A_18),converse(B_19)) = converse(join(A_18,B_19)) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_2794,plain,
! [B_108,A_109] : ( converse(join(B_108,A_109)) = converse(join(A_109,B_108)) ),
inference(superposition,[status(thm),theory(equality)],[c_2700,c_18]) ).
tff(c_3406,plain,
! [A_114,B_115] : ( converse(converse(join(A_114,B_115))) = join(B_115,A_114) ),
inference(superposition,[status(thm),theory(equality)],[c_2794,c_16]) ).
tff(c_3517,plain,
! [A_25] : ( join(meet(A_25,A_25),zero) = converse(converse(A_25)) ),
inference(superposition,[status(thm),theory(equality)],[c_1065,c_3406]) ).
tff(c_3574,plain,
! [A_25] : ( join(meet(A_25,A_25),zero) = A_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_3517]) ).
tff(c_4153,plain,
! [C_123] : ( join(complement(complement(C_123)),zero) = C_123 ),
inference(superposition,[status(thm),theory(equality)],[c_4129,c_3574]) ).
tff(c_4873,plain,
! [C_132] : ( join(C_132,zero) = C_132 ),
inference(demodulation,[status(thm),theory(equality)],[c_4487,c_4153]) ).
tff(c_669,plain,
! [B_61,A_62] : ( complement(join(complement(B_61),complement(A_62))) = meet(A_62,B_61) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_112]) ).
tff(c_696,plain,
! [B_61,A_62] : ( meet(B_61,A_62) = meet(A_62,B_61) ),
inference(superposition,[status(thm),theory(equality)],[c_669,c_8]) ).
tff(c_2187,plain,
! [A_100] : ( join(top,A_100) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_2136,c_1072]) ).
tff(c_2309,plain,
! [A_101] : ( join(A_101,top) = top ),
inference(superposition,[status(thm),theory(equality)],[c_2187,c_844]) ).
tff(c_2321,plain,
! [A_6] : ( join(meet(A_6,top),complement(top)) = A_6 ),
inference(superposition,[status(thm),theory(equality)],[c_2309,c_37]) ).
tff(c_2359,plain,
! [A_6] : ( join(zero,meet(A_6,top)) = A_6 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_149,c_2321]) ).
tff(c_3469,plain,
! [A_6] : ( join(meet(A_6,top),zero) = converse(converse(A_6)) ),
inference(superposition,[status(thm),theory(equality)],[c_2359,c_3406]) ).
tff(c_3735,plain,
! [A_118] : ( join(meet(A_118,top),zero) = A_118 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_3469]) ).
tff(c_3781,plain,
! [A_62] : ( join(meet(top,A_62),zero) = A_62 ),
inference(superposition,[status(thm),theory(equality)],[c_696,c_3735]) ).
tff(c_4883,plain,
! [A_62] : ( meet(top,A_62) = A_62 ),
inference(superposition,[status(thm),theory(equality)],[c_4873,c_3781]) ).
tff(c_4543,plain,
! [C_121] : ( join(zero,C_121) = C_121 ),
inference(demodulation,[status(thm),theory(equality)],[c_4487,c_4061]) ).
tff(c_327,plain,
! [A_17,B_46] : ( converse(join(converse(A_17),B_46)) = join(A_17,converse(B_46)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_306]) ).
tff(c_4921,plain,
! [A_17] : ( join(A_17,converse(zero)) = converse(converse(A_17)) ),
inference(superposition,[status(thm),theory(equality)],[c_4873,c_327]) ).
tff(c_5323,plain,
! [A_136] : ( join(A_136,converse(zero)) = A_136 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_4921]) ).
tff(c_5334,plain,
converse(zero) = zero,
inference(superposition,[status(thm),theory(equality)],[c_5323,c_4543]) ).
tff(c_427,plain,
! [A_52,B_53] : ( converse(join(converse(A_52),B_53)) = join(A_52,converse(B_53)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_306]) ).
tff(c_483,plain,
! [A_52] : ( join(A_52,converse(complement(converse(A_52)))) = converse(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_427]) ).
tff(c_2207,plain,
converse(top) = top,
inference(superposition,[status(thm),theory(equality)],[c_2187,c_483]) ).
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_65]) ).
tff(c_15899,plain,
! [A_226] : ( composition(top,converse(A_226)) = converse(composition(A_226,top)) ),
inference(superposition,[status(thm),theory(equality)],[c_2207,c_20]) ).
tff(c_15965,plain,
converse(composition(top,top)) = composition(top,top),
inference(superposition,[status(thm),theory(equality)],[c_2207,c_15899]) ).
tff(c_1237,plain,
! [A_77,B_78] : ( join(composition(converse(A_77),complement(composition(A_77,B_78))),complement(B_78)) = complement(B_78) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_1270,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_1237]) ).
tff(c_21646,plain,
! [A_260,B_261] : ( join(complement(converse(A_260)),composition(B_261,complement(converse(composition(A_260,B_261))))) = complement(converse(A_260)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16,c_1270]) ).
tff(c_21742,plain,
join(complement(converse(top)),composition(top,complement(composition(top,top)))) = complement(converse(top)),
inference(superposition,[status(thm),theory(equality)],[c_15965,c_21646]) ).
tff(c_21828,plain,
composition(top,complement(composition(top,top))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_4543,c_149,c_2207,c_149,c_2207,c_21742]) ).
tff(c_2198,plain,
! [A_63] : ( join(A_63,top) = top ),
inference(superposition,[status(thm),theory(equality)],[c_2187,c_844]) ).
tff(c_1099,plain,
! [A_73,C_74,B_75] : ( join(composition(A_73,C_74),composition(B_75,C_74)) = composition(join(A_73,B_75),C_74) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_1108,plain,
! [B_75,C_74,A_73] : ( join(composition(B_75,C_74),composition(A_73,C_74)) = composition(join(A_73,B_75),C_74) ),
inference(superposition,[status(thm),theory(equality)],[c_1099,c_2]) ).
tff(c_21854,plain,
! [A_73] : ( join(zero,composition(A_73,complement(composition(top,top)))) = composition(join(A_73,top),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_21828,c_1108]) ).
tff(c_21883,plain,
! [A_73] : ( composition(A_73,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_21828,c_4543,c_2198,c_21854]) ).
tff(c_21893,plain,
! [A_262] : ( composition(A_262,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_21828,c_4543,c_2198,c_21854]) ).
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_55]) ).
tff(c_21971,plain,
! [A_10,B_11] : ( composition(A_10,composition(B_11,complement(composition(top,top)))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_21893,c_10]) ).
tff(c_22024,plain,
! [A_263] : ( composition(A_263,zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_21883,c_21971]) ).
tff(c_374,plain,
! [A_17,B_48] : ( converse(composition(converse(A_17),B_48)) = composition(converse(B_48),A_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_362]) ).
tff(c_22054,plain,
! [A_17] : ( composition(converse(zero),A_17) = converse(zero) ),
inference(superposition,[status(thm),theory(equality)],[c_22024,c_374]) ).
tff(c_22110,plain,
! [A_17] : ( composition(zero,A_17) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_5334,c_5334,c_22054]) ).
tff(c_34,plain,
join(composition(complement(sk1),sk2),complement(sk3)) = complement(sk3),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_840,plain,
! [A_24,C_65] : ( join(A_24,join(complement(A_24),C_65)) = join(top,C_65) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_762]) ).
tff(c_5517,plain,
! [A_137,C_138] : ( join(A_137,join(complement(A_137),C_138)) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_2144,c_840]) ).
tff(c_5542,plain,
! [A_6,C_138] : ( join(meet(A_6,join(complement(complement(A_6)),C_138)),complement(top)) = A_6 ),
inference(superposition,[status(thm),theory(equality)],[c_5517,c_37]) ).
tff(c_5626,plain,
! [A_6,C_138] : ( meet(A_6,join(A_6,C_138)) = A_6 ),
inference(demodulation,[status(thm),theory(equality)],[c_4543,c_4487,c_2,c_149,c_5542]) ).
tff(c_6335,plain,
! [A_149,B_150,C_151] : ( join(join(A_149,B_150),C_151) = join(B_150,join(A_149,C_151)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_762]) ).
tff(c_6534,plain,
! [A_24,C_151] : ( join(complement(A_24),join(A_24,C_151)) = join(top,C_151) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_6335]) ).
tff(c_6565,plain,
! [A_152,C_153] : ( join(complement(A_152),join(A_152,C_153)) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_2144,c_6534]) ).
tff(c_7801,plain,
! [A_160,B_161] : ( join(complement(meet(A_160,B_161)),A_160) = top ),
inference(superposition,[status(thm),theory(equality)],[c_37,c_6565]) ).
tff(c_7878,plain,
! [B_9,B_161] : ( meet(meet(complement(B_9),B_161),B_9) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_7801,c_8]) ).
tff(c_9516,plain,
! [B_175,B_176] : ( meet(meet(complement(B_175),B_176),B_175) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_149,c_7878]) ).
tff(c_10621,plain,
! [B_186,B_187] : ( meet(meet(B_186,complement(B_187)),B_187) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_696,c_9516]) ).
tff(c_11928,plain,
! [B_199,C_200] : ( meet(meet(B_199,C_200),complement(C_200)) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_4487,c_10621]) ).
tff(c_13259,plain,
! [A_212,C_213] : ( meet(A_212,complement(join(A_212,C_213))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_5626,c_11928]) ).
tff(c_13493,plain,
meet(composition(complement(sk1),sk2),complement(complement(sk3))) = zero,
inference(superposition,[status(thm),theory(equality)],[c_34,c_13259]) ).
tff(c_13568,plain,
meet(sk3,composition(complement(sk1),sk2)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_696,c_4487,c_13493]) ).
tff(c_1883,plain,
! [A_89,A_17,C_91] : ( join(meet(composition(A_89,converse(A_17)),C_91),composition(meet(A_89,composition(C_91,A_17)),meet(converse(A_17),composition(converse(A_89),C_91)))) = composition(meet(A_89,composition(C_91,converse(converse(A_17)))),meet(converse(A_17),composition(converse(A_89),C_91))) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_1790]) ).
tff(c_33303,plain,
! [A_339,A_340,C_341] : ( join(meet(composition(A_339,converse(A_340)),C_341),composition(meet(A_339,composition(C_341,A_340)),meet(converse(A_340),composition(converse(A_339),C_341)))) = composition(meet(A_339,composition(C_341,A_340)),meet(converse(A_340),composition(converse(A_339),C_341))) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_1883]) ).
tff(c_33499,plain,
join(meet(composition(sk3,converse(sk2)),complement(sk1)),composition(zero,meet(converse(sk2),composition(converse(sk3),complement(sk1))))) = composition(meet(sk3,composition(complement(sk1),sk2)),meet(converse(sk2),composition(converse(sk3),complement(sk1)))),
inference(superposition,[status(thm),theory(equality)],[c_13568,c_33303]) ).
tff(c_33762,plain,
meet(complement(sk1),composition(sk3,converse(sk2))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_22110,c_4543,c_2,c_22110,c_13568,c_696,c_33499]) ).
tff(c_124,plain,
! [A_41,B_42] : ( join(join(complement(A_41),complement(B_42)),meet(A_41,B_42)) = top ),
inference(superposition,[status(thm),theory(equality)],[c_112,c_24]) ).
tff(c_64348,plain,
join(join(complement(complement(sk1)),complement(composition(sk3,converse(sk2)))),zero) = top,
inference(superposition,[status(thm),theory(equality)],[c_33762,c_124]) ).
tff(c_64418,plain,
join(sk1,complement(composition(sk3,converse(sk2)))) = top,
inference(demodulation,[status(thm),theory(equality)],[c_4543,c_2,c_4487,c_64348]) ).
tff(c_115,plain,
! [A_41,B_42,B_9] : ( meet(join(complement(A_41),complement(B_42)),B_9) = complement(join(meet(A_41,B_42),complement(B_9))) ),
inference(superposition,[status(thm),theory(equality)],[c_112,c_8]) ).
tff(c_1039,plain,
! [A_8,B_9,B_71] : ( join(meet(join(complement(A_8),complement(B_9)),B_71),complement(join(meet(A_8,B_9),B_71))) = join(complement(A_8),complement(B_9)) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_987]) ).
tff(c_27140,plain,
! [A_308,B_309,B_310] : ( join(complement(join(meet(A_308,B_309),B_310)),complement(join(meet(A_308,B_309),complement(B_310)))) = join(complement(A_308),complement(B_309)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_115,c_1039]) ).
tff(c_27570,plain,
! [A_308,B_309] : ( join(complement(join(meet(A_308,B_309),top)),complement(join(meet(A_308,B_309),zero))) = join(complement(A_308),complement(B_309)) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_27140]) ).
tff(c_298318,plain,
! [A_925,B_926] : ( join(complement(A_925),complement(B_926)) = complement(meet(A_925,B_926)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4543,c_4543,c_149,c_2144,c_2,c_2,c_27570]) ).
tff(c_299111,plain,
! [C_121,B_926] : ( complement(meet(complement(C_121),B_926)) = join(C_121,complement(B_926)) ),
inference(superposition,[status(thm),theory(equality)],[c_4487,c_298318]) ).
tff(c_4546,plain,
! [C_128] : ( complement(complement(C_128)) = C_128 ),
inference(superposition,[status(thm),theory(equality)],[c_4481,c_4061]) ).
tff(c_4591,plain,
! [A_8,C_128] : ( complement(join(complement(A_8),C_128)) = meet(A_8,complement(C_128)) ),
inference(superposition,[status(thm),theory(equality)],[c_4546,c_8]) ).
tff(c_1471,plain,
! [A_84,B_85] : ( join(A_84,join(B_85,complement(join(A_84,B_85)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_762]) ).
tff(c_1597,plain,
! [A_8,B_9] : ( join(complement(A_8),join(complement(B_9),meet(A_8,B_9))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1471]) ).
tff(c_1480,plain,
! [A_6,B_85] : ( join(meet(A_6,join(B_85,complement(join(complement(A_6),B_85)))),complement(top)) = A_6 ),
inference(superposition,[status(thm),theory(equality)],[c_1471,c_37]) ).
tff(c_113599,plain,
! [A_573,B_574] : ( join(zero,meet(A_573,join(B_574,complement(join(complement(A_573),B_574))))) = A_573 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_149,c_1480]) ).
tff(c_113866,plain,
! [A_8,B_9] : ( join(zero,meet(A_8,join(join(complement(B_9),meet(A_8,B_9)),complement(top)))) = A_8 ),
inference(superposition,[status(thm),theory(equality)],[c_1597,c_113599]) ).
tff(c_293987,plain,
! [A_918,B_919] : ( meet(A_918,join(complement(B_919),meet(A_918,B_919))) = A_918 ),
inference(demodulation,[status(thm),theory(equality)],[c_4543,c_4543,c_149,c_2,c_113866]) ).
tff(c_4220,plain,
! [C_123] : ( complement(join(zero,meet(C_123,C_123))) = meet(complement(C_123),top) ),
inference(superposition,[status(thm),theory(equality)],[c_4129,c_165]) ).
tff(c_4262,plain,
! [C_124] : ( meet(top,complement(C_124)) = complement(C_124) ),
inference(demodulation,[status(thm),theory(equality)],[c_1065,c_696,c_4220]) ).
tff(c_4294,plain,
! [B_42,A_41] : ( complement(join(complement(B_42),complement(A_41))) = meet(top,meet(A_41,B_42)) ),
inference(superposition,[status(thm),theory(equality)],[c_142,c_4262]) ).
tff(c_4317,plain,
! [A_41,B_42] : ( meet(top,meet(A_41,B_42)) = meet(B_42,A_41) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_4294]) ).
tff(c_294394,plain,
! [B_919,A_918] : ( meet(join(complement(B_919),meet(A_918,B_919)),A_918) = meet(top,A_918) ),
inference(superposition,[status(thm),theory(equality)],[c_293987,c_4317]) ).
tff(c_294934,plain,
! [B_919,A_918] : ( meet(join(complement(B_919),meet(A_918,B_919)),A_918) = A_918 ),
inference(demodulation,[status(thm),theory(equality)],[c_4883,c_294394]) ).
tff(c_408096,plain,
! [A_1093,C_1094] : ( complement(meet(A_1093,complement(C_1094))) = join(complement(A_1093),C_1094) ),
inference(superposition,[status(thm),theory(equality)],[c_4487,c_298318]) ).
tff(c_408621,plain,
! [B_919,C_1094] : ( join(complement(join(complement(B_919),meet(complement(C_1094),B_919))),C_1094) = complement(complement(C_1094)) ),
inference(superposition,[status(thm),theory(equality)],[c_294934,c_408096]) ).
tff(c_448420,plain,
! [C_1155,B_1156] : ( join(C_1155,meet(B_1156,join(C_1155,complement(B_1156)))) = C_1155 ),
inference(demodulation,[status(thm),theory(equality)],[c_299111,c_2,c_4591,c_4487,c_408621]) ).
tff(c_449400,plain,
join(sk1,meet(composition(sk3,converse(sk2)),top)) = sk1,
inference(superposition,[status(thm),theory(equality)],[c_64418,c_448420]) ).
tff(c_449779,plain,
join(sk1,composition(sk3,converse(sk2))) = sk1,
inference(demodulation,[status(thm),theory(equality)],[c_4883,c_696,c_449400]) ).
tff(c_449781,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_449779]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : REL044-2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 15:30:18 EDT 2023
% 0.14/0.35 % CPUTime :
% 132.50/110.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 132.59/110.19
% 132.59/110.19 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 132.95/110.24
% 132.95/110.24 Inference rules
% 132.95/110.24 ----------------------
% 132.95/110.24 #Ref : 0
% 132.95/110.24 #Sup : 112437
% 132.95/110.24 #Fact : 0
% 132.95/110.24 #Define : 0
% 132.95/110.24 #Split : 0
% 132.95/110.24 #Chain : 0
% 132.95/110.24 #Close : 0
% 132.95/110.24
% 132.95/110.24 Ordering : KBO
% 132.95/110.24
% 132.95/110.24 Simplification rules
% 132.95/110.24 ----------------------
% 132.95/110.24 #Subsume : 2238
% 132.95/110.24 #Demod : 190901
% 132.95/110.24 #Tautology : 60954
% 132.95/110.24 #SimpNegUnit : 1
% 132.95/110.24 #BackRed : 101
% 132.95/110.24
% 132.95/110.24 #Partial instantiations: 0
% 132.95/110.24 #Strategies tried : 1
% 132.95/110.24
% 132.95/110.24 Timing (in seconds)
% 132.95/110.24 ----------------------
% 132.95/110.24 Preprocessing : 0.52
% 132.95/110.24 Parsing : 0.28
% 132.95/110.24 CNF conversion : 0.02
% 132.95/110.24 Main loop : 108.56
% 132.95/110.24 Inferencing : 6.00
% 132.95/110.24 Reduction : 81.73
% 132.95/110.24 Demodulation : 78.15
% 132.95/110.24 BG Simplification : 0.71
% 132.95/110.24 Subsumption : 15.23
% 132.95/110.24 Abstraction : 1.54
% 132.95/110.24 MUC search : 0.00
% 132.95/110.24 Cooper : 0.00
% 132.95/110.24 Total : 109.17
% 132.95/110.24 Index Insertion : 0.00
% 132.95/110.25 Index Deletion : 0.00
% 132.95/110.25 Index Matching : 0.00
% 132.95/110.25 BG Taut test : 0.00
%------------------------------------------------------------------------------