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 : n026.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 10:54:28 EDT 2023
% Result : Theorem 18.58s 7.32s
% Output : CNFRefutation 18.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 24
% Syntax : Number of formulae : 190 ( 178 unt; 10 typ; 0 def)
% Number of atoms : 182 ( 180 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 1 |; 1 &)
% ( 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 240 (; 240 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ meet > join > composition > #nlpp > converse > complement > zero > top > one > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(top,type,
top: $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('#skF_2',type,
'#skF_2': $i ).
tff('#skF_1',type,
'#skF_1': $i ).
tff(one,type,
one: $i ).
tff(meet,type,
meet: ( $i * $i ) > $i ).
tff(zero,type,
zero: $i ).
tff(f_80,axiom,
! [X0] : ( zero = meet(X0,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
tff(f_78,axiom,
! [X0] : ( top = join(X0,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
tff(f_59,axiom,
! [X0,X1] : ( meet(X0,X1) = complement(join(complement(X0),complement(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
tff(f_53,axiom,
! [X0,X1] : ( join(X0,X1) = join(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
tff(f_57,axiom,
! [X0,X1] : ( X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
tff(f_69,axiom,
! [X0] : ( converse(converse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
tff(f_64,axiom,
! [X0] : ( composition(X0,one) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).
tff(f_73,axiom,
! [X0,X1] : ( converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
tff(f_62,axiom,
! [X0,X1,X2] : ( composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
tff(f_75,axiom,
! [X0,X1] : ( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
tff(f_55,axiom,
! [X0,X1,X2] : ( join(X0,join(X1,X2)) = join(join(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
tff(f_71,axiom,
! [X0,X1] : ( converse(join(X0,X1)) = join(converse(X0),converse(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
tff(f_66,axiom,
! [X0,X1,X2] : ( composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
tff(f_87,negated_conjecture,
~ ! [X0] :
( ( composition(X0,zero) = zero )
& ( composition(zero,X0) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(c_26,plain,
! [X0_25] : ( meet(X0_25,complement(X0_25)) = zero ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_24,plain,
! [X0_24] : ( join(X0_24,complement(X0_24)) = top ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_26812,plain,
! [X0_290,X1_291] : ( complement(join(complement(X0_290),complement(X1_291))) = meet(X0_290,X1_291) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_26846,plain,
! [X0_290] : ( meet(X0_290,complement(X0_290)) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_26812]) ).
tff(c_26849,plain,
complement(top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_26846]) ).
tff(c_2,plain,
! [X1_2,X0_1] : ( join(X1_2,X0_1) = join(X0_1,X1_2) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_8,plain,
! [X0_8,X1_9] : ( complement(join(complement(X0_8),complement(X1_9))) = meet(X0_8,X1_9) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_6,plain,
! [X0_6,X1_7] : ( join(complement(join(complement(X0_6),complement(X1_7))),complement(join(complement(X0_6),X1_7))) = X0_6 ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_27297,plain,
! [X0_310,X1_311] : ( join(meet(X0_310,X1_311),complement(join(complement(X0_310),X1_311))) = X0_310 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_27351,plain,
! [X0_310] : ( join(meet(X0_310,complement(complement(X0_310))),complement(top)) = X0_310 ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_27297]) ).
tff(c_27362,plain,
! [X0_310] : ( join(zero,meet(X0_310,complement(complement(X0_310)))) = X0_310 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26849,c_27351]) ).
tff(c_28539,plain,
! [X1_334,X0_335] : ( complement(join(complement(X1_334),complement(X0_335))) = meet(X0_335,X1_334) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_26812]) ).
tff(c_28590,plain,
! [X1_334,X0_335] : ( meet(X1_334,X0_335) = meet(X0_335,X1_334) ),
inference(superposition,[status(thm),theory(equality)],[c_28539,c_8]) ).
tff(c_28642,plain,
! [X1_334] : ( meet(complement(X1_334),X1_334) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_28539]) ).
tff(c_28650,plain,
! [X1_334] : ( meet(complement(X1_334),X1_334) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_26849,c_28642]) ).
tff(c_29888,plain,
! [X0_353,X1_354] : ( join(meet(X0_353,complement(X1_354)),meet(X0_353,X1_354)) = X0_353 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_27297]) ).
tff(c_29934,plain,
! [X1_354] : ( join(zero,meet(complement(complement(X1_354)),X1_354)) = complement(complement(X1_354)) ),
inference(superposition,[status(thm),theory(equality)],[c_28650,c_29888]) ).
tff(c_29970,plain,
! [X1_354] : ( complement(complement(X1_354)) = X1_354 ),
inference(demodulation,[status(thm),theory(equality)],[c_27362,c_28590,c_29934]) ).
tff(c_16,plain,
! [X0_17] : ( converse(converse(X0_17)) = X0_17 ),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_12,plain,
! [X0_13] : ( composition(X0_13,one) = X0_13 ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_26940,plain,
! [X1_295,X0_296] : ( composition(converse(X1_295),converse(X0_296)) = converse(composition(X0_296,X1_295)) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_29141,plain,
! [X0_343,X1_344] : ( converse(composition(converse(X0_343),X1_344)) = composition(converse(X1_344),X0_343) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_26940]) ).
tff(c_29194,plain,
! [X0_343] : ( composition(converse(one),X0_343) = converse(converse(X0_343)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_29141]) ).
tff(c_29207,plain,
! [X0_343] : ( composition(converse(one),X0_343) = X0_343 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_29194]) ).
tff(c_29609,plain,
! [X0_350] : ( composition(converse(one),X0_350) = X0_350 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_29194]) ).
tff(c_27057,plain,
! [X0_299,X1_300,X2_301] : ( composition(composition(X0_299,X1_300),X2_301) = composition(X0_299,composition(X1_300,X2_301)) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_27082,plain,
! [X0_13,X2_301] : ( composition(X0_13,composition(one,X2_301)) = composition(X0_13,X2_301) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_27057]) ).
tff(c_29636,plain,
! [X2_301] : ( composition(converse(one),X2_301) = composition(one,X2_301) ),
inference(superposition,[status(thm),theory(equality)],[c_29609,c_27082]) ).
tff(c_29667,plain,
! [X2_301] : ( composition(one,X2_301) = X2_301 ),
inference(demodulation,[status(thm),theory(equality)],[c_29207,c_29636]) ).
tff(c_29647,plain,
converse(one) = one,
inference(superposition,[status(thm),theory(equality)],[c_29609,c_12]) ).
tff(c_29718,plain,
! [X2_351] : ( composition(one,X2_351) = X2_351 ),
inference(demodulation,[status(thm),theory(equality)],[c_29207,c_29636]) ).
tff(c_22,plain,
! [X0_22,X1_23] : ( join(composition(converse(X0_22),complement(composition(X0_22,X1_23))),complement(X1_23)) = complement(X1_23) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_29734,plain,
! [X2_351] : ( join(composition(converse(one),complement(X2_351)),complement(X2_351)) = complement(X2_351) ),
inference(superposition,[status(thm),theory(equality)],[c_29718,c_22]) ).
tff(c_30856,plain,
! [X2_367] : ( join(complement(X2_367),complement(X2_367)) = complement(X2_367) ),
inference(demodulation,[status(thm),theory(equality)],[c_29667,c_2,c_29647,c_29734]) ).
tff(c_30883,plain,
! [X1_354] : ( join(X1_354,complement(complement(X1_354))) = complement(complement(X1_354)) ),
inference(superposition,[status(thm),theory(equality)],[c_29970,c_30856]) ).
tff(c_30930,plain,
! [X1_368] : ( join(X1_368,X1_368) = X1_368 ),
inference(demodulation,[status(thm),theory(equality)],[c_29970,c_29970,c_30883]) ).
tff(c_27158,plain,
! [X0_305,X1_306,X2_307] : ( join(join(X0_305,X1_306),X2_307) = join(X0_305,join(X1_306,X2_307)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_27174,plain,
! [X0_305,X1_306] : ( join(X0_305,join(X1_306,complement(join(X0_305,X1_306)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_27158,c_24]) ).
tff(c_30968,plain,
! [X1_368] : ( join(X1_368,join(X1_368,complement(X1_368))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_30930,c_27174]) ).
tff(c_31028,plain,
! [X1_368] : ( join(X1_368,top) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_30968]) ).
tff(c_27632,plain,
! [X0_320,X1_321] : ( join(X0_320,join(X1_321,complement(join(X0_320,X1_321)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_27158,c_24]) ).
tff(c_27748,plain,
! [X0_24] : ( join(X0_24,join(complement(X0_24),complement(top))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_27632]) ).
tff(c_27961,plain,
! [X0_325] : ( join(X0_325,join(zero,complement(X0_325))) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26849,c_27748]) ).
tff(c_28015,plain,
join(zero,top) = top,
inference(superposition,[status(thm),theory(equality)],[c_24,c_27961]) ).
tff(c_4,plain,
! [X0_3,X1_4,X2_5] : ( join(join(X0_3,X1_4),X2_5) = join(X0_3,join(X1_4,X2_5)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_28326,plain,
! [X2_332] : ( join(zero,join(top,X2_332)) = join(top,X2_332) ),
inference(superposition,[status(thm),theory(equality)],[c_28015,c_4]) ).
tff(c_28393,plain,
! [X1_2] : ( join(zero,join(X1_2,top)) = join(top,X1_2) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_28326]) ).
tff(c_31130,plain,
! [X1_370] : ( join(top,X1_370) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_31028,c_31028,c_28393]) ).
tff(c_26867,plain,
! [X0_292,X1_293] : ( join(converse(X0_292),converse(X1_293)) = converse(join(X0_292,X1_293)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_28096,plain,
! [X0_327,X1_328] : ( converse(join(converse(X0_327),X1_328)) = join(X0_327,converse(X1_328)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_26867]) ).
tff(c_28153,plain,
! [X0_327] : ( join(X0_327,converse(complement(converse(X0_327)))) = converse(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_28096]) ).
tff(c_31154,plain,
converse(top) = top,
inference(superposition,[status(thm),theory(equality)],[c_31130,c_28153]) ).
tff(c_26859,plain,
join(top,zero) = top,
inference(superposition,[status(thm),theory(equality)],[c_26849,c_24]) ).
tff(c_27212,plain,
! [X2_308] : ( join(top,join(zero,X2_308)) = join(top,X2_308) ),
inference(superposition,[status(thm),theory(equality)],[c_26859,c_27158]) ).
tff(c_27233,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm),theory(equality)],[c_24,c_27212]) ).
tff(c_26856,plain,
! [X0_8] : ( complement(join(complement(X0_8),zero)) = meet(X0_8,top) ),
inference(superposition,[status(thm),theory(equality)],[c_26849,c_8]) ).
tff(c_26902,plain,
! [X0_294] : ( complement(join(zero,complement(X0_294))) = meet(X0_294,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_26856]) ).
tff(c_26936,plain,
meet(zero,top) = complement(top),
inference(superposition,[status(thm),theory(equality)],[c_24,c_26902]) ).
tff(c_26939,plain,
meet(zero,top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26849,c_26936]) ).
tff(c_27324,plain,
join(zero,complement(join(complement(zero),top))) = zero,
inference(superposition,[status(thm),theory(equality)],[c_26939,c_27297]) ).
tff(c_27360,plain,
join(zero,complement(join(top,top))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_27233,c_2,c_27324]) ).
tff(c_27183,plain,
! [X2_307] : ( join(top,join(zero,X2_307)) = join(top,X2_307) ),
inference(superposition,[status(thm),theory(equality)],[c_26859,c_27158]) ).
tff(c_27383,plain,
join(top,complement(join(top,top))) = join(top,zero),
inference(superposition,[status(thm),theory(equality)],[c_27360,c_27183]) ).
tff(c_27395,plain,
join(top,complement(join(top,top))) = top,
inference(demodulation,[status(thm),theory(equality)],[c_26859,c_27383]) ).
tff(c_27682,plain,
join(top,top) = top,
inference(superposition,[status(thm),theory(equality)],[c_27395,c_27632]) ).
tff(c_27776,plain,
join(zero,complement(top)) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_27682,c_27360]) ).
tff(c_27779,plain,
join(zero,zero) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26849,c_27776]) ).
tff(c_28991,plain,
! [X2_342] : ( join(zero,join(zero,X2_342)) = join(zero,X2_342) ),
inference(superposition,[status(thm),theory(equality)],[c_27779,c_4]) ).
tff(c_29093,plain,
! [X0_310] : ( join(zero,meet(X0_310,complement(complement(X0_310)))) = join(zero,X0_310) ),
inference(superposition,[status(thm),theory(equality)],[c_27362,c_28991]) ).
tff(c_29138,plain,
! [X0_310] : ( join(zero,X0_310) = X0_310 ),
inference(demodulation,[status(thm),theory(equality)],[c_27362,c_29093]) ).
tff(c_26952,plain,
! [X0_17,X1_295] : ( converse(composition(converse(X0_17),X1_295)) = composition(converse(X1_295),X0_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_26940]) ).
tff(c_51512,plain,
! [X1_530] : ( composition(converse(X1_530),top) = converse(composition(top,X1_530)) ),
inference(superposition,[status(thm),theory(equality)],[c_31154,c_26952]) ).
tff(c_51563,plain,
converse(composition(top,top)) = composition(top,top),
inference(superposition,[status(thm),theory(equality)],[c_31154,c_51512]) ).
tff(c_20,plain,
! [X1_21,X0_20] : ( composition(converse(X1_21),converse(X0_20)) = converse(composition(X0_20,X1_21)) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_27397,plain,
! [X0_313,X1_314] : ( join(composition(converse(X0_313),complement(composition(X0_313,X1_314))),complement(X1_314)) = complement(X1_314) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_27430,plain,
! [X1_21,X0_20] : ( join(composition(converse(converse(X1_21)),complement(converse(composition(X0_20,X1_21)))),complement(converse(X0_20))) = complement(converse(X0_20)) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_27397]) ).
tff(c_55072,plain,
! [X0_551,X1_552] : ( join(complement(converse(X0_551)),composition(X1_552,complement(converse(composition(X0_551,X1_552))))) = complement(converse(X0_551)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16,c_27430]) ).
tff(c_55189,plain,
join(complement(converse(top)),composition(top,complement(composition(top,top)))) = complement(converse(top)),
inference(superposition,[status(thm),theory(equality)],[c_51563,c_55072]) ).
tff(c_55292,plain,
composition(top,complement(composition(top,top))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26849,c_31154,c_29138,c_26849,c_31154,c_55189]) ).
tff(c_27534,plain,
! [X0_316,X2_317,X1_318] : ( join(composition(X0_316,X2_317),composition(X1_318,X2_317)) = composition(join(X0_316,X1_318),X2_317) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_27585,plain,
! [X1_318,X2_317,X0_316] : ( join(composition(X1_318,X2_317),composition(X0_316,X2_317)) = composition(join(X0_316,X1_318),X2_317) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_27534]) ).
tff(c_55321,plain,
! [X0_316] : ( join(zero,composition(X0_316,complement(composition(top,top)))) = composition(join(X0_316,top),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_55292,c_27585]) ).
tff(c_55341,plain,
! [X0_316] : ( composition(X0_316,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_55292,c_31028,c_29138,c_55321]) ).
tff(c_10,plain,
! [X0_10,X1_11,X2_12] : ( composition(composition(X0_10,X1_11),X2_12) = composition(X0_10,composition(X1_11,X2_12)) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_55383,plain,
! [X0_553] : ( composition(X0_553,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_55292,c_31028,c_29138,c_55321]) ).
tff(c_55566,plain,
! [X0_10,X1_11] : ( composition(X0_10,composition(X1_11,complement(composition(top,top)))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_55383]) ).
tff(c_55612,plain,
! [X0_10] : ( composition(X0_10,zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_55341,c_55566]) ).
tff(c_104,plain,
! [X0_32,X1_33] : ( complement(join(complement(X0_32),complement(X1_33))) = meet(X0_32,X1_33) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_138,plain,
! [X0_32] : ( meet(X0_32,complement(X0_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,
! [X0_46,X1_47] : ( join(meet(X0_46,X1_47),complement(join(complement(X0_46),X1_47))) = X0_46 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_545,plain,
! [X0_46] : ( join(meet(X0_46,complement(complement(X0_46))),complement(top)) = X0_46 ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_491]) ).
tff(c_556,plain,
! [X0_46] : ( join(zero,meet(X0_46,complement(complement(X0_46)))) = X0_46 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_141,c_545]) ).
tff(c_2758,plain,
! [X1_83,X0_84] : ( complement(join(complement(X1_83),complement(X0_84))) = meet(X0_84,X1_83) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_104]) ).
tff(c_2827,plain,
! [X1_83,X0_84] : ( meet(X1_83,X0_84) = meet(X0_84,X1_83) ),
inference(superposition,[status(thm),theory(equality)],[c_2758,c_8]) ).
tff(c_18,plain,
! [X0_18,X1_19] : ( join(converse(X0_18),converse(X1_19)) = converse(join(X0_18,X1_19)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_159,plain,
! [X0_34,X1_35] : ( join(converse(X0_34),converse(X1_35)) = converse(join(X0_34,X1_35)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_1039,plain,
! [X1_63,X0_64] : ( join(converse(X1_63),converse(X0_64)) = converse(join(X0_64,X1_63)) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_2]) ).
tff(c_1110,plain,
! [X1_65,X0_66] : ( converse(join(X1_65,X0_66)) = converse(join(X0_66,X1_65)) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_1039]) ).
tff(c_1472,plain,
! [X1_71,X0_72] : ( converse(converse(join(X1_71,X0_72))) = join(X0_72,X1_71) ),
inference(superposition,[status(thm),theory(equality)],[c_1110,c_16]) ).
tff(c_1583,plain,
! [X0_24] : ( join(complement(X0_24),X0_24) = converse(converse(top)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_1472]) ).
tff(c_1617,plain,
! [X0_73] : ( join(complement(X0_73),X0_73) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_1583]) ).
tff(c_1648,plain,
! [X1_9] : ( meet(complement(X1_9),X1_9) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_1617,c_8]) ).
tff(c_1684,plain,
! [X1_9] : ( meet(complement(X1_9),X1_9) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_1648]) ).
tff(c_4004,plain,
! [X0_97,X1_98] : ( join(meet(X0_97,complement(X1_98)),meet(X0_97,X1_98)) = X0_97 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_491]) ).
tff(c_4061,plain,
! [X1_98] : ( join(zero,meet(complement(complement(X1_98)),X1_98)) = complement(complement(X1_98)) ),
inference(superposition,[status(thm),theory(equality)],[c_1684,c_4004]) ).
tff(c_4101,plain,
! [X1_98] : ( complement(complement(X1_98)) = X1_98 ),
inference(demodulation,[status(thm),theory(equality)],[c_556,c_2827,c_4061]) ).
tff(c_255,plain,
! [X1_37,X0_38] : ( composition(converse(X1_37),converse(X0_38)) = converse(composition(X0_38,X1_37)) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_5362,plain,
! [X0_111,X1_112] : ( converse(composition(converse(X0_111),X1_112)) = composition(converse(X1_112),X0_111) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_255]) ).
tff(c_5447,plain,
! [X0_111] : ( composition(converse(one),X0_111) = converse(converse(X0_111)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_5362]) ).
tff(c_5463,plain,
! [X0_111] : ( composition(converse(one),X0_111) = X0_111 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_5447]) ).
tff(c_5465,plain,
! [X0_113] : ( composition(converse(one),X0_113) = X0_113 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_5447]) ).
tff(c_591,plain,
! [X0_49,X1_50,X2_51] : ( composition(composition(X0_49,X1_50),X2_51) = composition(X0_49,composition(X1_50,X2_51)) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_613,plain,
! [X0_13,X2_51] : ( composition(X0_13,composition(one,X2_51)) = composition(X0_13,X2_51) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_591]) ).
tff(c_5486,plain,
! [X2_51] : ( composition(converse(one),X2_51) = composition(one,X2_51) ),
inference(superposition,[status(thm),theory(equality)],[c_5465,c_613]) ).
tff(c_5523,plain,
! [X2_51] : ( composition(one,X2_51) = X2_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,
! [X2_115] : ( composition(one,X2_115) = X2_115 ),
inference(demodulation,[status(thm),theory(equality)],[c_5463,c_5486]) ).
tff(c_5683,plain,
! [X2_115] : ( join(composition(converse(one),complement(X2_115)),complement(X2_115)) = complement(X2_115) ),
inference(superposition,[status(thm),theory(equality)],[c_5673,c_22]) ).
tff(c_5876,plain,
! [X2_117] : ( join(complement(X2_117),complement(X2_117)) = complement(X2_117) ),
inference(demodulation,[status(thm),theory(equality)],[c_5523,c_2,c_5503,c_5683]) ).
tff(c_29,plain,
! [X0_6,X1_7] : ( join(meet(X0_6,X1_7),complement(join(complement(X0_6),X1_7))) = X0_6 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_5894,plain,
! [X2_117] : ( join(meet(X2_117,complement(X2_117)),complement(complement(X2_117))) = X2_117 ),
inference(superposition,[status(thm),theory(equality)],[c_5876,c_29]) ).
tff(c_6259,plain,
! [X2_121] : ( join(zero,X2_121) = X2_121 ),
inference(demodulation,[status(thm),theory(equality)],[c_4101,c_26,c_5894]) ).
tff(c_183,plain,
! [X0_34,X0_17] : ( converse(join(X0_34,converse(X0_17))) = join(converse(X0_34),X0_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_159]) ).
tff(c_6286,plain,
! [X0_17] : ( join(converse(zero),X0_17) = converse(converse(X0_17)) ),
inference(superposition,[status(thm),theory(equality)],[c_6259,c_183]) ).
tff(c_7591,plain,
! [X0_134] : ( join(converse(zero),X0_134) = X0_134 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_6286]) ).
tff(c_6328,plain,
! [X2_121] : ( join(X2_121,zero) = X2_121 ),
inference(superposition,[status(thm),theory(equality)],[c_6259,c_2]) ).
tff(c_7609,plain,
converse(zero) = zero,
inference(superposition,[status(thm),theory(equality)],[c_7591,c_6328]) ).
tff(c_5906,plain,
! [X1_98] : ( join(X1_98,complement(complement(X1_98))) = complement(complement(X1_98)) ),
inference(superposition,[status(thm),theory(equality)],[c_4101,c_5876]) ).
tff(c_6927,plain,
! [X1_128] : ( join(X1_128,X1_128) = X1_128 ),
inference(demodulation,[status(thm),theory(equality)],[c_4101,c_4101,c_5906]) ).
tff(c_349,plain,
! [X0_41,X1_42,X2_43] : ( join(join(X0_41,X1_42),X2_43) = join(X0_41,join(X1_42,X2_43)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_398,plain,
! [X0_41,X1_42] : ( join(X0_41,join(X1_42,complement(join(X0_41,X1_42)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_349]) ).
tff(c_6991,plain,
! [X1_128] : ( join(X1_128,join(X1_128,complement(X1_128))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_6927,c_398]) ).
tff(c_7150,plain,
! [X1_130] : ( join(X1_130,top) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_6991]) ).
tff(c_1167,plain,
! [X1_65,X0_66] : ( converse(converse(join(X1_65,X0_66))) = join(X0_66,X1_65) ),
inference(superposition,[status(thm),theory(equality)],[c_1110,c_16]) ).
tff(c_7188,plain,
! [X1_130] : ( join(top,X1_130) = converse(converse(top)) ),
inference(superposition,[status(thm),theory(equality)],[c_7150,c_1167]) ).
tff(c_7280,plain,
! [X1_131] : ( join(top,X1_131) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_7188]) ).
tff(c_4792,plain,
! [X0_106,X1_107] : ( converse(join(converse(X0_106),X1_107)) = join(X0_106,converse(X1_107)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_159]) ).
tff(c_4906,plain,
! [X0_106] : ( join(X0_106,converse(complement(converse(X0_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,
! [X0_8,X0_32,X1_33] : ( meet(X0_8,join(complement(X0_32),complement(X1_33))) = complement(join(complement(X0_8),meet(X0_32,X1_33))) ),
inference(superposition,[status(thm),theory(equality)],[c_104,c_8]) ).
tff(c_5951,plain,
! [X2_117] : ( join(zero,X2_117) = X2_117 ),
inference(demodulation,[status(thm),theory(equality)],[c_4101,c_26,c_5894]) ).
tff(c_119,plain,
! [X0_32,X1_33] : ( meet(join(complement(X0_32),complement(X1_33)),meet(X0_32,X1_33)) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_104,c_26]) ).
tff(c_799,plain,
! [X0_59,X1_60] : ( join(composition(converse(X0_59),complement(composition(X0_59,X1_60))),complement(X1_60)) = complement(X1_60) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_838,plain,
! [X0_59,X0_8,X1_9] : ( join(composition(converse(X0_59),complement(composition(X0_59,join(complement(X0_8),complement(X1_9))))),meet(X0_8,X1_9)) = complement(join(complement(X0_8),complement(X1_9))) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_799]) ).
tff(c_24870,plain,
! [X0_279,X0_280,X1_281] : ( join(composition(converse(X0_279),complement(composition(X0_279,join(complement(X0_280),complement(X1_281))))),meet(X0_280,X1_281)) = meet(X0_280,X1_281) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_838]) ).
tff(c_25061,plain,
! [X0_279,X0_32,X1_33] : ( join(composition(converse(X0_279),complement(composition(X0_279,join(complement(join(complement(X0_32),complement(X1_33))),complement(meet(X0_32,X1_33)))))),zero) = meet(join(complement(X0_32),complement(X1_33)),meet(X0_32,X1_33)) ),
inference(superposition,[status(thm),theory(equality)],[c_119,c_24870]) ).
tff(c_25247,plain,
! [X0_282] : ( composition(converse(X0_282),complement(composition(X0_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,
! [X1_130] : ( join(top,X1_130) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_7188]) ).
tff(c_14,plain,
! [X0_14,X2_16,X1_15] : ( join(composition(X0_14,X2_16),composition(X1_15,X2_16)) = composition(join(X0_14,X1_15),X2_16) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_25460,plain,
! [X1_15] : ( join(zero,composition(X1_15,complement(composition(top,top)))) = composition(join(top,X1_15),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_25341,c_14]) ).
tff(c_25483,plain,
! [X1_15] : ( composition(X1_15,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_25341,c_7259,c_5951,c_25460]) ).
tff(c_25736,plain,
! [X1_284] : ( composition(X1_284,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_25341,c_7259,c_5951,c_25460]) ).
tff(c_695,plain,
! [X0_53,X2_54,X1_55] : ( join(composition(X0_53,X2_54),composition(X1_55,X2_54)) = composition(join(X0_53,X1_55),X2_54) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_716,plain,
! [X0_53,X2_12,X0_10,X1_11] : ( join(composition(X0_53,X2_12),composition(X0_10,composition(X1_11,X2_12))) = composition(join(X0_53,composition(X0_10,X1_11)),X2_12) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_695]) ).
tff(c_25751,plain,
! [X0_10,X1_11,X1_284] : ( join(zero,composition(X0_10,composition(X1_11,complement(composition(top,top))))) = composition(join(X1_284,composition(X0_10,X1_11)),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_25736,c_716]) ).
tff(c_25884,plain,
! [X0_285] : ( composition(X0_285,zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_25483,c_25483,c_5951,c_25751]) ).
tff(c_267,plain,
! [X0_17,X1_37] : ( converse(composition(converse(X0_17),X1_37)) = composition(converse(X1_37),X0_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_255]) ).
tff(c_25947,plain,
! [X0_17] : ( composition(converse(zero),X0_17) = converse(zero) ),
inference(superposition,[status(thm),theory(equality)],[c_25884,c_267]) ).
tff(c_25993,plain,
! [X0_17] : ( composition(zero,X0_17) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_7609,c_7609,c_25947]) ).
tff(c_28,plain,
( ( composition('#skF_2',zero) != zero )
| ( composition(zero,'#skF_1') != zero ) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_103,plain,
composition(zero,'#skF_1') != zero,
inference(splitLeft,[status(thm)],[c_28]) ).
tff(c_26805,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_25993,c_103]) ).
tff(c_26806,plain,
composition('#skF_2',zero) != zero,
inference(splitRight,[status(thm)],[c_28]) ).
tff(c_55791,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_55612,c_26806]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL013+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % 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
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 15:53:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 18.58/7.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.58/7.33
% 18.58/7.33 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.83/7.39
% 18.83/7.39 Inference rules
% 18.83/7.39 ----------------------
% 18.83/7.39 #Ref : 0
% 18.83/7.39 #Sup : 14034
% 18.83/7.39 #Fact : 0
% 18.83/7.39 #Define : 0
% 18.83/7.39 #Split : 1
% 18.83/7.39 #Chain : 0
% 18.83/7.39 #Close : 0
% 18.83/7.39
% 18.83/7.39 Ordering : KBO
% 18.83/7.39
% 18.83/7.39 Simplification rules
% 18.83/7.39 ----------------------
% 18.83/7.39 #Subsume : 202
% 18.83/7.39 #Demod : 18681
% 18.83/7.39 #Tautology : 8678
% 18.83/7.39 #SimpNegUnit : 0
% 18.83/7.39 #BackRed : 106
% 18.83/7.39
% 18.83/7.39 #Partial instantiations: 0
% 18.83/7.39 #Strategies tried : 1
% 18.83/7.39
% 18.83/7.39 Timing (in seconds)
% 18.83/7.39 ----------------------
% 18.83/7.39 Preprocessing : 0.48
% 18.83/7.39 Parsing : 0.26
% 18.83/7.39 CNF conversion : 0.03
% 18.83/7.39 Main loop : 5.82
% 18.83/7.39 Inferencing : 1.15
% 18.83/7.39 Reduction : 3.40
% 18.83/7.39 Demodulation : 3.08
% 18.83/7.39 BG Simplification : 0.11
% 18.83/7.39 Subsumption : 0.83
% 18.83/7.39 Abstraction : 0.18
% 18.83/7.39 MUC search : 0.00
% 18.83/7.39 Cooper : 0.00
% 18.83/7.39 Total : 6.38
% 18.83/7.39 Index Insertion : 0.00
% 18.83/7.39 Index Deletion : 0.00
% 18.83/7.39 Index Matching : 0.00
% 18.83/7.39 BG Taut test : 0.00
%------------------------------------------------------------------------------