TSTP Solution File: REL013-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : REL013-1 : 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/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 : 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 10:54:27 EDT 2023
% Result : Unsatisfiable 18.95s 7.67s
% Output : CNFRefutation 19.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 23
% Syntax : Number of formulae : 187 ( 176 unt; 9 typ; 0 def)
% Number of atoms : 180 ( 178 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 225 (; 225 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ meet > join > composition > #nlpp > converse > complement > zero > top > sk1 > one
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(top,type,
top: $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(zero,type,
zero: $i ).
tff(f_61,axiom,
! [A] : ( converse(converse(A)) = A ),
file(unknown,unknown) ).
tff(f_47,axiom,
! [A,B] : ( join(A,B) = join(B,A) ),
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_51,axiom,
! [A,B] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
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_63,axiom,
! [A,B] : ( converse(join(A,B)) = join(converse(A),converse(B)) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [A] : ( composition(A,one) = A ),
file(unknown,unknown) ).
tff(f_65,axiom,
! [A,B] : ( converse(composition(A,B)) = composition(converse(B),converse(A)) ),
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_59,axiom,
! [A,B,C] : ( composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ),
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_78,axiom,
( ( composition(sk1,zero) != zero )
| ( composition(zero,sk1) != zero ) ),
file(unknown,unknown) ).
tff(c_16,plain,
! [A_17] : ( converse(converse(A_17)) = A_17 ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
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_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_25893,plain,
! [A_285,B_286] : ( complement(join(complement(A_285),complement(B_286))) = meet(A_285,B_286) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_25927,plain,
! [A_285] : ( meet(A_285,complement(A_285)) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_25893]) ).
tff(c_25930,plain,
complement(top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_25927]) ).
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_26377,plain,
! [A_305,B_306] : ( join(meet(A_305,B_306),complement(join(complement(A_305),B_306))) = A_305 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_26431,plain,
! [A_305] : ( join(meet(A_305,complement(complement(A_305))),complement(top)) = A_305 ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_26377]) ).
tff(c_26442,plain,
! [A_305] : ( join(zero,meet(A_305,complement(complement(A_305)))) = A_305 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_25930,c_26431]) ).
tff(c_25967,plain,
join(top,zero) = top,
inference(superposition,[status(thm),theory(equality)],[c_25930,c_24]) ).
tff(c_26235,plain,
! [A_300,B_301,C_302] : ( join(join(A_300,B_301),C_302) = join(A_300,join(B_301,C_302)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_26289,plain,
! [C_303] : ( join(top,join(zero,C_303)) = join(top,C_303) ),
inference(superposition,[status(thm),theory(equality)],[c_25967,c_26235]) ).
tff(c_26310,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm),theory(equality)],[c_24,c_26289]) ).
tff(c_25964,plain,
! [A_8] : ( complement(join(complement(A_8),zero)) = meet(A_8,top) ),
inference(superposition,[status(thm),theory(equality)],[c_25930,c_8]) ).
tff(c_26055,plain,
! [A_292] : ( complement(join(zero,complement(A_292))) = meet(A_292,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_25964]) ).
tff(c_26104,plain,
meet(zero,top) = complement(top),
inference(superposition,[status(thm),theory(equality)],[c_24,c_26055]) ).
tff(c_26108,plain,
meet(zero,top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_25930,c_26104]) ).
tff(c_26398,plain,
join(zero,complement(join(complement(zero),top))) = zero,
inference(superposition,[status(thm),theory(equality)],[c_26108,c_26377]) ).
tff(c_26440,plain,
join(zero,complement(join(top,top))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26310,c_2,c_26398]) ).
tff(c_26260,plain,
! [C_302] : ( join(top,join(zero,C_302)) = join(top,C_302) ),
inference(superposition,[status(thm),theory(equality)],[c_25967,c_26235]) ).
tff(c_26463,plain,
join(top,complement(join(top,top))) = join(top,zero),
inference(superposition,[status(thm),theory(equality)],[c_26440,c_26260]) ).
tff(c_26475,plain,
join(top,complement(join(top,top))) = top,
inference(demodulation,[status(thm),theory(equality)],[c_25967,c_26463]) ).
tff(c_25973,plain,
! [A_8] : ( complement(join(zero,complement(A_8))) = meet(A_8,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_25964]) ).
tff(c_26469,plain,
meet(join(top,top),top) = complement(zero),
inference(superposition,[status(thm),theory(equality)],[c_26440,c_25973]) ).
tff(c_29,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_26559,plain,
join(complement(zero),complement(join(complement(join(top,top)),top))) = join(top,top),
inference(superposition,[status(thm),theory(equality)],[c_26469,c_29]) ).
tff(c_26568,plain,
join(top,top) = top,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_25930,c_2,c_26475,c_2,c_26559]) ).
tff(c_26575,plain,
join(zero,complement(top)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26568,c_26440]) ).
tff(c_26578,plain,
join(zero,zero) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_25930,c_26575]) ).
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_49]) ).
tff(c_27425,plain,
! [C_326] : ( join(zero,join(zero,C_326)) = join(zero,C_326) ),
inference(superposition,[status(thm),theory(equality)],[c_26578,c_4]) ).
tff(c_27493,plain,
! [A_305] : ( join(zero,meet(A_305,complement(complement(A_305)))) = join(zero,A_305) ),
inference(superposition,[status(thm),theory(equality)],[c_26442,c_27425]) ).
tff(c_27531,plain,
! [A_305] : ( join(zero,A_305) = A_305 ),
inference(demodulation,[status(thm),theory(equality)],[c_26442,c_27493]) ).
tff(c_25931,plain,
! [A_287,B_288] : ( join(converse(A_287),converse(B_288)) = converse(join(A_287,B_288)) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_28429,plain,
! [A_344,A_345] : ( converse(join(A_344,converse(A_345))) = join(converse(A_344),A_345) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_25931]) ).
tff(c_28490,plain,
! [A_345] : ( join(converse(zero),A_345) = converse(converse(A_345)) ),
inference(superposition,[status(thm),theory(equality)],[c_27531,c_28429]) ).
tff(c_28519,plain,
! [A_346] : ( join(converse(zero),A_346) = A_346 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_28490]) ).
tff(c_27544,plain,
! [A_327] : ( join(zero,A_327) = A_327 ),
inference(demodulation,[status(thm),theory(equality)],[c_26442,c_27493]) ).
tff(c_27587,plain,
! [A_327] : ( join(A_327,zero) = A_327 ),
inference(superposition,[status(thm),theory(equality)],[c_27544,c_2]) ).
tff(c_28538,plain,
converse(zero) = zero,
inference(superposition,[status(thm),theory(equality)],[c_28519,c_27587]) ).
tff(c_25961,plain,
! [B_9] : ( complement(join(zero,complement(B_9))) = meet(top,B_9) ),
inference(superposition,[status(thm),theory(equality)],[c_25930,c_8]) ).
tff(c_27542,plain,
! [B_9] : ( complement(complement(B_9)) = meet(top,B_9) ),
inference(demodulation,[status(thm),theory(equality)],[c_27531,c_25961]) ).
tff(c_12,plain,
! [A_13] : ( composition(A_13,one) = A_13 ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_25983,plain,
! [B_289,A_290] : ( composition(converse(B_289),converse(A_290)) = converse(composition(A_290,B_289)) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_27696,plain,
! [A_329,B_330] : ( converse(composition(converse(A_329),B_330)) = composition(converse(B_330),A_329) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_25983]) ).
tff(c_27737,plain,
! [A_329] : ( composition(converse(one),A_329) = converse(converse(A_329)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_27696]) ).
tff(c_27824,plain,
! [A_332] : ( composition(converse(one),A_332) = A_332 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_27737]) ).
tff(c_27858,plain,
converse(one) = one,
inference(superposition,[status(thm),theory(equality)],[c_27824,c_12]) ).
tff(c_27750,plain,
! [A_329] : ( composition(converse(one),A_329) = A_329 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_27737]) ).
tff(c_27883,plain,
! [A_329] : ( composition(one,A_329) = A_329 ),
inference(demodulation,[status(thm),theory(equality)],[c_27858,c_27750]) ).
tff(c_27984,plain,
! [A_335] : ( composition(one,A_335) = A_335 ),
inference(demodulation,[status(thm),theory(equality)],[c_27858,c_27750]) ).
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_27994,plain,
! [A_335] : ( join(composition(converse(one),complement(A_335)),complement(A_335)) = complement(A_335) ),
inference(superposition,[status(thm),theory(equality)],[c_27984,c_22]) ).
tff(c_28755,plain,
! [A_348] : ( join(complement(A_348),complement(A_348)) = complement(A_348) ),
inference(demodulation,[status(thm),theory(equality)],[c_27883,c_2,c_27858,c_27994]) ).
tff(c_28767,plain,
! [A_348] : ( join(meet(A_348,complement(A_348)),complement(complement(A_348))) = A_348 ),
inference(superposition,[status(thm),theory(equality)],[c_28755,c_29]) ).
tff(c_28816,plain,
! [A_348] : ( meet(top,A_348) = A_348 ),
inference(demodulation,[status(thm),theory(equality)],[c_27542,c_27531,c_26,c_28767]) ).
tff(c_28833,plain,
! [B_9] : ( complement(complement(B_9)) = B_9 ),
inference(demodulation,[status(thm),theory(equality)],[c_28816,c_27542]) ).
tff(c_28904,plain,
! [B_350] : ( complement(complement(B_350)) = B_350 ),
inference(demodulation,[status(thm),theory(equality)],[c_28816,c_27542]) ).
tff(c_28017,plain,
! [A_335] : ( join(complement(A_335),complement(A_335)) = complement(A_335) ),
inference(demodulation,[status(thm),theory(equality)],[c_27883,c_2,c_27858,c_27994]) ).
tff(c_28916,plain,
! [B_350] : ( join(complement(complement(B_350)),B_350) = complement(complement(B_350)) ),
inference(superposition,[status(thm),theory(equality)],[c_28904,c_28017]) ).
tff(c_29046,plain,
! [B_352] : ( join(B_352,B_352) = B_352 ),
inference(demodulation,[status(thm),theory(equality)],[c_28833,c_28833,c_28916]) ).
tff(c_26284,plain,
! [A_300,B_301] : ( join(A_300,join(B_301,complement(join(A_300,B_301)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_26235]) ).
tff(c_29080,plain,
! [B_352] : ( join(B_352,join(B_352,complement(B_352))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_29046,c_26284]) ).
tff(c_29139,plain,
! [B_352] : ( join(B_352,top) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_29080]) ).
tff(c_26735,plain,
! [A_314,B_315] : ( join(A_314,join(B_315,complement(join(A_314,B_315)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_26235]) ).
tff(c_26839,plain,
! [A_24] : ( join(A_24,join(complement(A_24),complement(top))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_26735]) ).
tff(c_26864,plain,
! [A_316] : ( join(A_316,join(zero,complement(A_316))) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_25930,c_26839]) ).
tff(c_26914,plain,
join(zero,top) = top,
inference(superposition,[status(thm),theory(equality)],[c_24,c_26864]) ).
tff(c_26975,plain,
! [C_318] : ( join(zero,join(top,C_318)) = join(top,C_318) ),
inference(superposition,[status(thm),theory(equality)],[c_26914,c_4]) ).
tff(c_27031,plain,
! [B_2] : ( join(zero,join(B_2,top)) = join(top,B_2) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_26975]) ).
tff(c_29445,plain,
! [B_357] : ( join(top,B_357) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_29139,c_29139,c_27031]) ).
tff(c_25955,plain,
! [A_287,A_17] : ( converse(join(A_287,converse(A_17))) = join(converse(A_287),A_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_25931]) ).
tff(c_29668,plain,
! [A_360] : ( join(converse(top),A_360) = converse(top) ),
inference(superposition,[status(thm),theory(equality)],[c_29445,c_25955]) ).
tff(c_29676,plain,
converse(top) = top,
inference(superposition,[status(thm),theory(equality)],[c_29668,c_29139]) ).
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_56684,plain,
! [A_543] : ( composition(top,converse(A_543)) = converse(composition(A_543,top)) ),
inference(superposition,[status(thm),theory(equality)],[c_29676,c_20]) ).
tff(c_56738,plain,
converse(composition(top,top)) = composition(top,top),
inference(superposition,[status(thm),theory(equality)],[c_29676,c_56684]) ).
tff(c_26605,plain,
! [A_311,B_312] : ( join(composition(converse(A_311),complement(composition(A_311,B_312))),complement(B_312)) = complement(B_312) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_26638,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_26605]) ).
tff(c_53584,plain,
! [A_528,B_529] : ( join(complement(converse(A_528)),composition(B_529,complement(converse(composition(A_528,B_529))))) = complement(converse(A_528)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16,c_26638]) ).
tff(c_53746,plain,
! [B_529] : ( join(complement(top),composition(B_529,complement(converse(composition(top,B_529))))) = complement(converse(top)) ),
inference(superposition,[status(thm),theory(equality)],[c_29676,c_53584]) ).
tff(c_53841,plain,
! [B_529] : ( composition(B_529,complement(converse(composition(top,B_529)))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_25930,c_29676,c_27531,c_25930,c_53746]) ).
tff(c_56786,plain,
composition(top,complement(composition(top,top))) = zero,
inference(superposition,[status(thm),theory(equality)],[c_56738,c_53841]) ).
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_59]) ).
tff(c_56930,plain,
! [A_14] : ( join(composition(A_14,complement(composition(top,top))),zero) = composition(join(A_14,top),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_56786,c_14]) ).
tff(c_56943,plain,
! [A_14] : ( composition(A_14,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_56786,c_29139,c_27587,c_56930]) ).
tff(c_56983,plain,
! [A_544] : ( composition(A_544,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_56786,c_29139,c_27587,c_56930]) ).
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_57052,plain,
! [A_10,B_11] : ( composition(A_10,composition(B_11,complement(composition(top,top)))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_56983,c_10]) ).
tff(c_57110,plain,
! [A_545] : ( composition(A_545,zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_56943,c_57052]) ).
tff(c_25995,plain,
! [A_17,B_289] : ( converse(composition(converse(A_17),B_289)) = composition(converse(B_289),A_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_25983]) ).
tff(c_57148,plain,
! [A_17] : ( composition(converse(zero),A_17) = converse(zero) ),
inference(superposition,[status(thm),theory(equality)],[c_57110,c_25995]) ).
tff(c_57189,plain,
! [A_17] : ( composition(zero,A_17) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_28538,c_28538,c_57148]) ).
tff(c_104,plain,
! [A_32,B_33] : ( complement(join(complement(A_32),complement(B_33))) = meet(A_32,B_33) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_138,plain,
! [A_32] : ( meet(A_32,complement(A_32)) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_104]) ).
tff(c_141,plain,
complement(top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_138]) ).
tff(c_491,plain,
! [A_46,B_47] : ( join(meet(A_46,B_47),complement(join(complement(A_46),B_47))) = A_46 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_545,plain,
! [A_46] : ( join(meet(A_46,complement(complement(A_46))),complement(top)) = A_46 ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_491]) ).
tff(c_556,plain,
! [A_46] : ( join(zero,meet(A_46,complement(complement(A_46)))) = A_46 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_141,c_545]) ).
tff(c_2758,plain,
! [B_83,A_84] : ( complement(join(complement(B_83),complement(A_84))) = meet(A_84,B_83) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_104]) ).
tff(c_2827,plain,
! [B_83,A_84] : ( meet(B_83,A_84) = meet(A_84,B_83) ),
inference(superposition,[status(thm),theory(equality)],[c_2758,c_8]) ).
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_159,plain,
! [A_34,B_35] : ( join(converse(A_34),converse(B_35)) = converse(join(A_34,B_35)) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_1039,plain,
! [B_63,A_64] : ( join(converse(B_63),converse(A_64)) = converse(join(A_64,B_63)) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_2]) ).
tff(c_1110,plain,
! [B_65,A_66] : ( converse(join(B_65,A_66)) = converse(join(A_66,B_65)) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_1039]) ).
tff(c_1472,plain,
! [B_71,A_72] : ( converse(converse(join(B_71,A_72))) = join(A_72,B_71) ),
inference(superposition,[status(thm),theory(equality)],[c_1110,c_16]) ).
tff(c_1583,plain,
! [A_24] : ( join(complement(A_24),A_24) = converse(converse(top)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_1472]) ).
tff(c_1617,plain,
! [A_73] : ( join(complement(A_73),A_73) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_1583]) ).
tff(c_1648,plain,
! [B_9] : ( meet(complement(B_9),B_9) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_1617,c_8]) ).
tff(c_1684,plain,
! [B_9] : ( meet(complement(B_9),B_9) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_1648]) ).
tff(c_4004,plain,
! [A_97,B_98] : ( join(meet(A_97,complement(B_98)),meet(A_97,B_98)) = A_97 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_491]) ).
tff(c_4061,plain,
! [B_98] : ( join(zero,meet(complement(complement(B_98)),B_98)) = complement(complement(B_98)) ),
inference(superposition,[status(thm),theory(equality)],[c_1684,c_4004]) ).
tff(c_4101,plain,
! [B_98] : ( complement(complement(B_98)) = B_98 ),
inference(demodulation,[status(thm),theory(equality)],[c_556,c_2827,c_4061]) ).
tff(c_255,plain,
! [B_37,A_38] : ( composition(converse(B_37),converse(A_38)) = converse(composition(A_38,B_37)) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_5362,plain,
! [A_111,B_112] : ( converse(composition(converse(A_111),B_112)) = composition(converse(B_112),A_111) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_255]) ).
tff(c_5447,plain,
! [A_111] : ( composition(converse(one),A_111) = converse(converse(A_111)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_5362]) ).
tff(c_5463,plain,
! [A_111] : ( composition(converse(one),A_111) = A_111 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_5447]) ).
tff(c_5465,plain,
! [A_113] : ( composition(converse(one),A_113) = A_113 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_5447]) ).
tff(c_591,plain,
! [A_49,B_50,C_51] : ( composition(composition(A_49,B_50),C_51) = composition(A_49,composition(B_50,C_51)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_613,plain,
! [A_13,C_51] : ( composition(A_13,composition(one,C_51)) = composition(A_13,C_51) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_591]) ).
tff(c_5486,plain,
! [C_51] : ( composition(converse(one),C_51) = composition(one,C_51) ),
inference(superposition,[status(thm),theory(equality)],[c_5465,c_613]) ).
tff(c_5523,plain,
! [C_51] : ( composition(one,C_51) = C_51 ),
inference(demodulation,[status(thm),theory(equality)],[c_5463,c_5486]) ).
tff(c_5503,plain,
converse(one) = one,
inference(superposition,[status(thm),theory(equality)],[c_5465,c_12]) ).
tff(c_5673,plain,
! [C_115] : ( composition(one,C_115) = C_115 ),
inference(demodulation,[status(thm),theory(equality)],[c_5463,c_5486]) ).
tff(c_5683,plain,
! [C_115] : ( join(composition(converse(one),complement(C_115)),complement(C_115)) = complement(C_115) ),
inference(superposition,[status(thm),theory(equality)],[c_5673,c_22]) ).
tff(c_5876,plain,
! [C_117] : ( join(complement(C_117),complement(C_117)) = complement(C_117) ),
inference(demodulation,[status(thm),theory(equality)],[c_5523,c_2,c_5503,c_5683]) ).
tff(c_5906,plain,
! [B_98] : ( join(B_98,complement(complement(B_98))) = complement(complement(B_98)) ),
inference(superposition,[status(thm),theory(equality)],[c_4101,c_5876]) ).
tff(c_6927,plain,
! [B_128] : ( join(B_128,B_128) = B_128 ),
inference(demodulation,[status(thm),theory(equality)],[c_4101,c_4101,c_5906]) ).
tff(c_349,plain,
! [A_41,B_42,C_43] : ( join(join(A_41,B_42),C_43) = join(A_41,join(B_42,C_43)) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_398,plain,
! [A_41,B_42] : ( join(A_41,join(B_42,complement(join(A_41,B_42)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_349]) ).
tff(c_6991,plain,
! [B_128] : ( join(B_128,join(B_128,complement(B_128))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_6927,c_398]) ).
tff(c_7150,plain,
! [B_130] : ( join(B_130,top) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_6991]) ).
tff(c_1167,plain,
! [B_65,A_66] : ( converse(converse(join(B_65,A_66))) = join(A_66,B_65) ),
inference(superposition,[status(thm),theory(equality)],[c_1110,c_16]) ).
tff(c_7188,plain,
! [B_130] : ( join(top,B_130) = converse(converse(top)) ),
inference(superposition,[status(thm),theory(equality)],[c_7150,c_1167]) ).
tff(c_7280,plain,
! [B_131] : ( join(top,B_131) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_7188]) ).
tff(c_4792,plain,
! [A_106,B_107] : ( converse(join(converse(A_106),B_107)) = join(A_106,converse(B_107)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_159]) ).
tff(c_4906,plain,
! [A_106] : ( join(A_106,converse(complement(converse(A_106)))) = converse(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_4792]) ).
tff(c_7303,plain,
converse(top) = top,
inference(superposition,[status(thm),theory(equality)],[c_7280,c_4906]) ).
tff(c_110,plain,
! [A_8,A_32,B_33] : ( meet(A_8,join(complement(A_32),complement(B_33))) = complement(join(complement(A_8),meet(A_32,B_33))) ),
inference(superposition,[status(thm),theory(equality)],[c_104,c_8]) ).
tff(c_5894,plain,
! [C_117] : ( join(meet(C_117,complement(C_117)),complement(complement(C_117))) = C_117 ),
inference(superposition,[status(thm),theory(equality)],[c_5876,c_29]) ).
tff(c_5951,plain,
! [C_117] : ( join(zero,C_117) = C_117 ),
inference(demodulation,[status(thm),theory(equality)],[c_4101,c_26,c_5894]) ).
tff(c_119,plain,
! [A_32,B_33] : ( meet(join(complement(A_32),complement(B_33)),meet(A_32,B_33)) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_104,c_26]) ).
tff(c_799,plain,
! [A_59,B_60] : ( join(composition(converse(A_59),complement(composition(A_59,B_60))),complement(B_60)) = complement(B_60) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_838,plain,
! [A_59,A_8,B_9] : ( join(composition(converse(A_59),complement(composition(A_59,join(complement(A_8),complement(B_9))))),meet(A_8,B_9)) = complement(join(complement(A_8),complement(B_9))) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_799]) ).
tff(c_24870,plain,
! [A_279,A_280,B_281] : ( join(composition(converse(A_279),complement(composition(A_279,join(complement(A_280),complement(B_281))))),meet(A_280,B_281)) = meet(A_280,B_281) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_838]) ).
tff(c_25061,plain,
! [A_279,A_32,B_33] : ( join(composition(converse(A_279),complement(composition(A_279,join(complement(join(complement(A_32),complement(B_33))),complement(meet(A_32,B_33)))))),zero) = meet(join(complement(A_32),complement(B_33)),meet(A_32,B_33)) ),
inference(superposition,[status(thm),theory(equality)],[c_119,c_24870]) ).
tff(c_25247,plain,
! [A_282] : ( composition(converse(A_282),complement(composition(A_282,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_24,c_2,c_110,c_5951,c_2827,c_24,c_2,c_8,c_2,c_2,c_25061]) ).
tff(c_25341,plain,
composition(top,complement(composition(top,top))) = zero,
inference(superposition,[status(thm),theory(equality)],[c_7303,c_25247]) ).
tff(c_7259,plain,
! [B_130] : ( join(top,B_130) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_7188]) ).
tff(c_25460,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_25341,c_14]) ).
tff(c_25483,plain,
! [B_15] : ( composition(B_15,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_25341,c_7259,c_5951,c_25460]) ).
tff(c_25736,plain,
! [B_284] : ( composition(B_284,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_25341,c_7259,c_5951,c_25460]) ).
tff(c_695,plain,
! [A_53,C_54,B_55] : ( join(composition(A_53,C_54),composition(B_55,C_54)) = composition(join(A_53,B_55),C_54) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_716,plain,
! [A_53,C_12,A_10,B_11] : ( join(composition(A_53,C_12),composition(A_10,composition(B_11,C_12))) = composition(join(A_53,composition(A_10,B_11)),C_12) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_695]) ).
tff(c_25751,plain,
! [A_10,B_11,B_284] : ( join(zero,composition(A_10,composition(B_11,complement(composition(top,top))))) = composition(join(B_284,composition(A_10,B_11)),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_25736,c_716]) ).
tff(c_25851,plain,
! [A_10] : ( composition(A_10,zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_25483,c_25483,c_5951,c_25751]) ).
tff(c_28,plain,
( ( composition(zero,sk1) != zero )
| ( composition(sk1,zero) != zero ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_103,plain,
composition(sk1,zero) != zero,
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_25886,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_25851,c_103]) ).
tff(c_25887,plain,
composition(zero,sk1) != zero,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_57357,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_57189,c_25887]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL013-1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % 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
% 0.09/0.33 % Computer : n022.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8042.1875MB
% 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Thu Aug 3 15:42:18 EDT 2023
% 0.09/0.33 % CPUTime :
% 18.95/7.67 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.04/7.69
% 19.04/7.69 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.04/7.74
% 19.04/7.74 Inference rules
% 19.04/7.74 ----------------------
% 19.04/7.74 #Ref : 0
% 19.04/7.74 #Sup : 14369
% 19.04/7.74 #Fact : 0
% 19.04/7.74 #Define : 0
% 19.04/7.74 #Split : 1
% 19.04/7.74 #Chain : 0
% 19.04/7.74 #Close : 0
% 19.04/7.74
% 19.28/7.74 Ordering : KBO
% 19.28/7.74
% 19.28/7.74 Simplification rules
% 19.28/7.74 ----------------------
% 19.28/7.74 #Subsume : 218
% 19.28/7.74 #Demod : 19063
% 19.28/7.74 #Tautology : 9083
% 19.28/7.74 #SimpNegUnit : 0
% 19.28/7.74 #BackRed : 111
% 19.28/7.74
% 19.28/7.74 #Partial instantiations: 0
% 19.28/7.74 #Strategies tried : 1
% 19.28/7.74
% 19.28/7.74 Timing (in seconds)
% 19.28/7.74 ----------------------
% 19.28/7.74 Preprocessing : 0.60
% 19.28/7.74 Parsing : 0.32
% 19.28/7.74 CNF conversion : 0.03
% 19.28/7.74 Main loop : 6.01
% 19.28/7.74 Inferencing : 1.20
% 19.28/7.74 Reduction : 3.50
% 19.28/7.74 Demodulation : 3.17
% 19.28/7.74 BG Simplification : 0.12
% 19.28/7.74 Subsumption : 0.85
% 19.28/7.74 Abstraction : 0.18
% 19.28/7.74 MUC search : 0.00
% 19.28/7.74 Cooper : 0.00
% 19.28/7.74 Total : 6.69
% 19.28/7.74 Index Insertion : 0.00
% 19.28/7.74 Index Deletion : 0.00
% 19.28/7.74 Index Matching : 0.00
% 19.28/7.74 BG Taut test : 0.00
%------------------------------------------------------------------------------