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/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 : n012.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 10:54:38 EDT 2023
% Result : Theorem 69.50s 55.06s
% Output : CNFRefutation 69.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 26
% Syntax : Number of formulae : 154 ( 142 unt; 11 typ; 0 def)
% Number of atoms : 144 ( 143 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 207 (; 207 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ meet > join > composition > #nlpp > converse > complement > zero > top > one > #skF_2 > #skF_3 > #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_3',type,
'#skF_3': $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_53,axiom,
! [X0,X1] : ( join(X0,X1) = join(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
tff(f_120,negated_conjecture,
~ ! [X0,X1,X2] :
( ( join(composition(complement(X0),X1),complement(X2)) = complement(X2) )
=> ( join(composition(X2,converse(X1)),X0) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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_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_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_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_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_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_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_108,axiom,
! [X0,X1,X2] : ( join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+1.ax',dedekind_law) ).
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_34,plain,
join(composition('#skF_3',converse('#skF_2')),'#skF_1') != '#skF_1',
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_38,plain,
join('#skF_1',composition('#skF_3',converse('#skF_2'))) != '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_2,c_34]) ).
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_370,plain,
! [X1_48,X0_49] : ( composition(converse(X1_48),converse(X0_49)) = converse(composition(X0_49,X1_48)) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_431,plain,
! [X0_52,X1_53] : ( converse(composition(converse(X0_52),X1_53)) = composition(converse(X1_53),X0_52) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_370]) ).
tff(c_471,plain,
! [X0_52] : ( composition(converse(one),X0_52) = converse(converse(X0_52)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_431]) ).
tff(c_481,plain,
! [X0_54] : ( composition(converse(one),X0_54) = X0_54 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_471]) ).
tff(c_495,plain,
converse(one) = one,
inference(superposition,[status(thm),theory(equality)],[c_481,c_12]) ).
tff(c_479,plain,
! [X0_52] : ( composition(converse(one),X0_52) = X0_52 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_471]) ).
tff(c_585,plain,
! [X0_52] : ( composition(one,X0_52) = X0_52 ),
inference(demodulation,[status(thm),theory(equality)],[c_495,c_479]) ).
tff(c_1082,plain,
! [X0_72,X1_73] : ( join(composition(converse(X0_72),complement(composition(X0_72,X1_73))),complement(X1_73)) = complement(X1_73) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_1106,plain,
! [X0_52] : ( join(composition(converse(one),complement(X0_52)),complement(X0_52)) = complement(X0_52) ),
inference(superposition,[status(thm),theory(equality)],[c_585,c_1082]) ).
tff(c_1157,plain,
! [X0_74] : ( join(complement(X0_74),complement(X0_74)) = complement(X0_74) ),
inference(demodulation,[status(thm),theory(equality)],[c_585,c_2,c_495,c_1106]) ).
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_1322,plain,
! [X0_77] : ( meet(X0_77,X0_77) = complement(complement(X0_77)) ),
inference(superposition,[status(thm),theory(equality)],[c_1157,c_8]) ).
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_112,plain,
! [X0_41,X1_42] : ( complement(join(complement(X0_41),complement(X1_42))) = meet(X0_41,X1_42) ),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_146,plain,
! [X0_41] : ( meet(X0_41,complement(X0_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_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_670,plain,
! [X0_60,X1_61] : ( join(meet(X0_60,X1_61),complement(join(complement(X0_60),X1_61))) = X0_60 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_727,plain,
! [X0_60] : ( join(meet(X0_60,complement(complement(X0_60))),complement(top)) = X0_60 ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_670]) ).
tff(c_738,plain,
! [X0_60] : ( join(zero,meet(X0_60,complement(complement(X0_60)))) = X0_60 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_149,c_727]) ).
tff(c_1352,plain,
! [X0_77] : ( join(zero,meet(X0_77,meet(X0_77,X0_77))) = X0_77 ),
inference(superposition,[status(thm),theory(equality)],[c_1322,c_738]) ).
tff(c_1193,plain,
join(zero,complement(top)) = complement(top),
inference(superposition,[status(thm),theory(equality)],[c_149,c_1157]) ).
tff(c_1212,plain,
join(zero,zero) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_149,c_149,c_1193]) ).
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_2547,plain,
! [X2_104] : ( join(zero,join(zero,X2_104)) = join(zero,X2_104) ),
inference(superposition,[status(thm),theory(equality)],[c_1212,c_4]) ).
tff(c_2568,plain,
! [X0_77] : ( join(zero,meet(X0_77,meet(X0_77,X0_77))) = join(zero,X0_77) ),
inference(superposition,[status(thm),theory(equality)],[c_1352,c_2547]) ).
tff(c_2614,plain,
! [X0_105] : ( join(zero,X0_105) = X0_105 ),
inference(demodulation,[status(thm),theory(equality)],[c_1352,c_2568]) ).
tff(c_730,plain,
! [X0_25] : ( join(zero,complement(join(complement(X0_25),complement(X0_25)))) = X0_25 ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_670]) ).
tff(c_739,plain,
! [X0_25] : ( join(zero,meet(X0_25,X0_25)) = X0_25 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_730]) ).
tff(c_2640,plain,
! [X0_25] : ( meet(X0_25,X0_25) = X0_25 ),
inference(superposition,[status(thm),theory(equality)],[c_2614,c_739]) ).
tff(c_1169,plain,
! [X0_74] : ( meet(X0_74,X0_74) = complement(complement(X0_74)) ),
inference(superposition,[status(thm),theory(equality)],[c_1157,c_8]) ).
tff(c_3013,plain,
! [X0_74] : ( complement(complement(X0_74)) = X0_74 ),
inference(demodulation,[status(thm),theory(equality)],[c_2640,c_1169]) ).
tff(c_2602,plain,
! [X0_77] : ( join(zero,X0_77) = X0_77 ),
inference(demodulation,[status(thm),theory(equality)],[c_1352,c_2568]) ).
tff(c_3430,plain,
! [X1_115,X0_116] : ( complement(join(complement(X1_115),complement(X0_116))) = meet(X0_116,X1_115) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_112]) ).
tff(c_3512,plain,
! [X0_116] : ( complement(join(zero,complement(X0_116))) = meet(X0_116,top) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_3430]) ).
tff(c_3543,plain,
! [X0_116] : ( meet(X0_116,top) = X0_116 ),
inference(demodulation,[status(thm),theory(equality)],[c_3013,c_2602,c_3512]) ).
tff(c_306,plain,
! [X0_45,X1_46] : ( join(converse(X0_45),converse(X1_46)) = converse(join(X0_45,X1_46)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_330,plain,
! [X0_45,X0_17] : ( converse(join(X0_45,converse(X0_17))) = join(converse(X0_45),X0_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_306]) ).
tff(c_2647,plain,
! [X0_17] : ( join(converse(zero),X0_17) = converse(converse(X0_17)) ),
inference(superposition,[status(thm),theory(equality)],[c_2614,c_330]) ).
tff(c_3884,plain,
! [X0_121] : ( join(converse(zero),X0_121) = X0_121 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_2647]) ).
tff(c_2679,plain,
! [X1_2] : ( join(X1_2,zero) = X1_2 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_2614]) ).
tff(c_3907,plain,
converse(zero) = zero,
inference(superposition,[status(thm),theory(equality)],[c_3884,c_2679]) ).
tff(c_3157,plain,
! [X0_111] : ( complement(complement(X0_111)) = X0_111 ),
inference(demodulation,[status(thm),theory(equality)],[c_2640,c_1169]) ).
tff(c_1148,plain,
! [X0_52] : ( join(complement(X0_52),complement(X0_52)) = complement(X0_52) ),
inference(demodulation,[status(thm),theory(equality)],[c_585,c_2,c_495,c_1106]) ).
tff(c_3187,plain,
! [X0_111] : ( join(complement(complement(X0_111)),X0_111) = complement(complement(X0_111)) ),
inference(superposition,[status(thm),theory(equality)],[c_3157,c_1148]) ).
tff(c_3229,plain,
! [X0_111] : ( join(X0_111,X0_111) = X0_111 ),
inference(demodulation,[status(thm),theory(equality)],[c_3013,c_3013,c_3187]) ).
tff(c_512,plain,
! [X0_55,X1_56,X2_57] : ( join(join(X0_55,X1_56),X2_57) = join(X0_55,join(X1_56,X2_57)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_5079,plain,
! [X0_134,X1_135] : ( join(X0_134,join(X1_135,complement(join(X0_134,X1_135)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_512]) ).
tff(c_5176,plain,
! [X0_111] : ( join(X0_111,join(X0_111,complement(X0_111))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_3229,c_5079]) ).
tff(c_5324,plain,
! [X0_136] : ( join(X0_136,top) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_5176]) ).
tff(c_5430,plain,
! [X0_137] : ( join(top,X0_137) = top ),
inference(superposition,[status(thm),theory(equality)],[c_5324,c_2]) ).
tff(c_4699,plain,
! [X0_130,X1_131] : ( converse(join(converse(X0_130),X1_131)) = join(X0_130,converse(X1_131)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_306]) ).
tff(c_4815,plain,
! [X0_130] : ( join(X0_130,converse(complement(converse(X0_130)))) = converse(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_4699]) ).
tff(c_5447,plain,
converse(top) = top,
inference(superposition,[status(thm),theory(equality)],[c_5430,c_4815]) ).
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_38572,plain,
! [X0_323] : ( composition(top,converse(X0_323)) = converse(composition(X0_323,top)) ),
inference(superposition,[status(thm),theory(equality)],[c_5447,c_20]) ).
tff(c_38644,plain,
converse(composition(top,top)) = composition(top,top),
inference(superposition,[status(thm),theory(equality)],[c_5447,c_38572]) ).
tff(c_1118,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_1082]) ).
tff(c_33008,plain,
! [X0_297,X1_298] : ( join(complement(converse(X0_297)),composition(X1_298,complement(converse(composition(X0_297,X1_298))))) = complement(converse(X0_297)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16,c_1118]) ).
tff(c_33152,plain,
! [X1_298] : ( join(complement(top),composition(X1_298,complement(converse(composition(top,X1_298))))) = complement(converse(top)) ),
inference(superposition,[status(thm),theory(equality)],[c_5447,c_33008]) ).
tff(c_33237,plain,
! [X1_298] : ( composition(X1_298,complement(converse(composition(top,X1_298)))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_149,c_5447,c_2602,c_149,c_33152]) ).
tff(c_38701,plain,
composition(top,complement(composition(top,top))) = zero,
inference(superposition,[status(thm),theory(equality)],[c_38644,c_33237]) ).
tff(c_5302,plain,
! [X0_111] : ( join(X0_111,top) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_5176]) ).
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_38868,plain,
! [X0_14] : ( join(composition(X0_14,complement(composition(top,top))),zero) = composition(join(X0_14,top),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_38701,c_14]) ).
tff(c_38886,plain,
! [X0_14] : ( composition(X0_14,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_38701,c_5302,c_2679,c_38868]) ).
tff(c_39432,plain,
! [X0_328] : ( composition(X0_328,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_38701,c_5302,c_2679,c_38868]) ).
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_39508,plain,
! [X0_10,X1_11] : ( composition(X0_10,composition(X1_11,complement(composition(top,top)))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_39432,c_10]) ).
tff(c_39568,plain,
! [X0_329] : ( composition(X0_329,zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_38886,c_39508]) ).
tff(c_382,plain,
! [X0_17,X1_48] : ( converse(composition(converse(X0_17),X1_48)) = composition(converse(X1_48),X0_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_370]) ).
tff(c_39637,plain,
! [X0_17] : ( composition(converse(zero),X0_17) = converse(zero) ),
inference(superposition,[status(thm),theory(equality)],[c_39568,c_382]) ).
tff(c_39667,plain,
! [X0_17] : ( composition(zero,X0_17) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_3907,c_3907,c_39637]) ).
tff(c_5382,plain,
! [X0_136] : ( join(top,X0_136) = top ),
inference(superposition,[status(thm),theory(equality)],[c_5324,c_2]) ).
tff(c_576,plain,
! [X0_24,X2_57] : ( join(X0_24,join(complement(X0_24),X2_57)) = join(top,X2_57) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_512]) ).
tff(c_5631,plain,
! [X0_138,X2_139] : ( join(X0_138,join(complement(X0_138),X2_139)) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_5382,c_576]) ).
tff(c_6422,plain,
! [X0_146,X1_147] : ( join(X0_146,join(X1_147,complement(X0_146))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_5631]) ).
tff(c_36,plain,
join(composition(complement('#skF_1'),'#skF_2'),complement('#skF_3')) = complement('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_556,plain,
! [X2_57] : ( join(composition(complement('#skF_1'),'#skF_2'),join(complement('#skF_3'),X2_57)) = join(complement('#skF_3'),X2_57) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_512]) ).
tff(c_6482,plain,
join(complement('#skF_3'),complement(composition(complement('#skF_1'),'#skF_2'))) = top,
inference(superposition,[status(thm),theory(equality)],[c_6422,c_556]) ).
tff(c_8234,plain,
meet('#skF_3',composition(complement('#skF_1'),'#skF_2')) = complement(top),
inference(superposition,[status(thm),theory(equality)],[c_6482,c_8]) ).
tff(c_8251,plain,
meet('#skF_3',composition(complement('#skF_1'),'#skF_2')) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_149,c_8234]) ).
tff(c_3524,plain,
! [X1_9,X0_8] : ( meet(X1_9,X0_8) = meet(X0_8,X1_9) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_3430]) ).
tff(c_2424,plain,
! [X0_101,X1_102,X2_103] : ( join(meet(composition(X0_101,X1_102),X2_103),composition(meet(X0_101,composition(X2_103,converse(X1_102))),meet(X1_102,composition(converse(X0_101),X2_103)))) = composition(meet(X0_101,composition(X2_103,converse(X1_102))),meet(X1_102,composition(converse(X0_101),X2_103))) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_2518,plain,
! [X0_101,X0_17,X2_103] : ( join(meet(composition(X0_101,converse(X0_17)),X2_103),composition(meet(X0_101,composition(X2_103,X0_17)),meet(converse(X0_17),composition(converse(X0_101),X2_103)))) = composition(meet(X0_101,composition(X2_103,converse(converse(X0_17)))),meet(converse(X0_17),composition(converse(X0_101),X2_103))) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_2424]) ).
tff(c_67752,plain,
! [X0_456,X0_457,X2_458] : ( join(meet(composition(X0_456,converse(X0_457)),X2_458),composition(meet(X0_456,composition(X2_458,X0_457)),meet(converse(X0_457),composition(converse(X0_456),X2_458)))) = composition(meet(X0_456,composition(X2_458,X0_457)),meet(converse(X0_457),composition(converse(X0_456),X2_458))) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_2518]) ).
tff(c_68081,plain,
join(meet(composition('#skF_3',converse('#skF_2')),complement('#skF_1')),composition(zero,meet(converse('#skF_2'),composition(converse('#skF_3'),complement('#skF_1'))))) = composition(meet('#skF_3',composition(complement('#skF_1'),'#skF_2')),meet(converse('#skF_2'),composition(converse('#skF_3'),complement('#skF_1')))),
inference(superposition,[status(thm),theory(equality)],[c_8251,c_67752]) ).
tff(c_68321,plain,
meet(complement('#skF_1'),composition('#skF_3',converse('#skF_2'))) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_39667,c_2602,c_2,c_39667,c_8251,c_3524,c_68081]) ).
tff(c_115,plain,
! [X0_41,X1_42,X1_9] : ( meet(join(complement(X0_41),complement(X1_42)),X1_9) = complement(join(meet(X0_41,X1_42),complement(X1_9))) ),
inference(superposition,[status(thm),theory(equality)],[c_112,c_8]) ).
tff(c_712,plain,
! [X0_8,X1_9,X1_61] : ( join(meet(join(complement(X0_8),complement(X1_9)),X1_61),complement(join(meet(X0_8,X1_9),X1_61))) = join(complement(X0_8),complement(X1_9)) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_670]) ).
tff(c_44320,plain,
! [X0_8,X1_9,X1_61] : ( join(complement(join(meet(X0_8,X1_9),X1_61)),complement(join(meet(X0_8,X1_9),complement(X1_61)))) = join(complement(X0_8),complement(X1_9)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_115,c_712]) ).
tff(c_111336,plain,
! [X1_61] : ( join(complement(join(meet(complement('#skF_1'),composition('#skF_3',converse('#skF_2'))),X1_61)),complement(join(zero,complement(X1_61)))) = join(complement(complement('#skF_1')),complement(composition('#skF_3',converse('#skF_2')))) ),
inference(superposition,[status(thm),theory(equality)],[c_68321,c_44320]) ).
tff(c_111431,plain,
join('#skF_1',complement(composition('#skF_3',converse('#skF_2')))) = top,
inference(demodulation,[status(thm),theory(equality)],[c_24,c_2602,c_68321,c_3013,c_3013,c_2,c_2602,c_111336]) ).
tff(c_1448,plain,
! [X0_79,X2_80,X1_81] : ( join(composition(X0_79,X2_80),composition(X1_81,X2_80)) = composition(join(X0_79,X1_81),X2_80) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_18273,plain,
! [X1_232,X2_233,X0_234] : ( join(composition(X1_232,X2_233),composition(X0_234,X2_233)) = composition(join(X0_234,X1_232),X2_233) ),
inference(superposition,[status(thm),theory(equality)],[c_1448,c_2]) ).
tff(c_125216,plain,
! [X1_612,X0_613,X2_614] : ( composition(join(X1_612,X0_613),X2_614) = composition(join(X0_613,X1_612),X2_614) ),
inference(superposition,[status(thm),theory(equality)],[c_18273,c_14]) ).
tff(c_129149,plain,
! [X1_620,X0_621] : ( composition(join(X1_620,X0_621),one) = join(X0_621,X1_620) ),
inference(superposition,[status(thm),theory(equality)],[c_125216,c_12]) ).
tff(c_129376,plain,
join(complement(composition('#skF_3',converse('#skF_2'))),'#skF_1') = composition(top,one),
inference(superposition,[status(thm),theory(equality)],[c_111431,c_129149]) ).
tff(c_129949,plain,
join(complement(composition('#skF_3',converse('#skF_2'))),'#skF_1') = top,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_129376]) ).
tff(c_3515,plain,
! [X1_115] : ( complement(join(complement(X1_115),zero)) = meet(top,X1_115) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_3430]) ).
tff(c_3544,plain,
! [X1_115] : ( meet(top,X1_115) = X1_115 ),
inference(demodulation,[status(thm),theory(equality)],[c_3013,c_2602,c_2,c_3515]) ).
tff(c_29143,plain,
! [X0_281,X1_282,X1_283] : ( meet(join(complement(X0_281),complement(X1_282)),X1_283) = complement(join(meet(X0_281,X1_282),complement(X1_283))) ),
inference(superposition,[status(thm),theory(equality)],[c_112,c_8]) ).
tff(c_29399,plain,
! [X1_282,X1_283] : ( complement(join(meet(top,X1_282),complement(X1_283))) = meet(join(zero,complement(X1_282)),X1_283) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_29143]) ).
tff(c_29483,plain,
! [X1_282,X1_283] : ( complement(join(X1_282,complement(X1_283))) = meet(complement(X1_282),X1_283) ),
inference(demodulation,[status(thm),theory(equality)],[c_3544,c_2602,c_29399]) ).
tff(c_30552,plain,
! [X0_287,X0_288,X1_289] : ( meet(X0_287,join(complement(X0_288),complement(X1_289))) = complement(join(complement(X0_287),meet(X0_288,X1_289))) ),
inference(superposition,[status(thm),theory(equality)],[c_112,c_8]) ).
tff(c_30805,plain,
! [X0_287,X1_289] : ( complement(join(complement(X0_287),meet(top,X1_289))) = meet(X0_287,join(zero,complement(X1_289))) ),
inference(superposition,[status(thm),theory(equality)],[c_149,c_30552]) ).
tff(c_223517,plain,
! [X0_794,X1_795] : ( complement(join(complement(X0_794),X1_795)) = meet(X0_794,complement(X1_795)) ),
inference(demodulation,[status(thm),theory(equality)],[c_3544,c_2602,c_30805]) ).
tff(c_224133,plain,
! [X0_74,X1_795] : ( meet(complement(X0_74),complement(X1_795)) = complement(join(X0_74,X1_795)) ),
inference(superposition,[status(thm),theory(equality)],[c_3013,c_223517]) ).
tff(c_124,plain,
! [X0_41,X1_42] : ( join(join(complement(X0_41),complement(X1_42)),meet(X0_41,X1_42)) = top ),
inference(superposition,[status(thm),theory(equality)],[c_112,c_24]) ).
tff(c_9862,plain,
! [X0_178,X1_179,X2_180] : ( join(join(X0_178,X1_179),X2_180) = join(X1_179,join(X0_178,X2_180)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_512]) ).
tff(c_105524,plain,
! [X1_569,X0_570] : ( join(complement(X1_569),join(complement(X0_570),meet(X0_570,X1_569))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_124,c_9862]) ).
tff(c_37,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_105798,plain,
! [X1_569,X0_570] : ( join(meet(X1_569,join(complement(X0_570),meet(X0_570,X1_569))),complement(top)) = X1_569 ),
inference(superposition,[status(thm),theory(equality)],[c_105524,c_37]) ).
tff(c_211506,plain,
! [X1_771,X0_772] : ( meet(X1_771,join(complement(X0_772),meet(X0_772,X1_771))) = X1_771 ),
inference(demodulation,[status(thm),theory(equality)],[c_2602,c_2,c_149,c_105798]) ).
tff(c_261599,plain,
! [X1_863,X0_864] : ( meet(X1_863,join(X0_864,meet(complement(X0_864),X1_863))) = X1_863 ),
inference(superposition,[status(thm),theory(equality)],[c_3013,c_211506]) ).
tff(c_221751,plain,
! [X1_789,X1_790] : ( complement(join(X1_789,complement(X1_790))) = meet(complement(X1_789),X1_790) ),
inference(demodulation,[status(thm),theory(equality)],[c_3544,c_2602,c_29399]) ).
tff(c_222086,plain,
! [X1_789,X1_790] : ( complement(meet(complement(X1_789),X1_790)) = join(X1_789,complement(X1_790)) ),
inference(superposition,[status(thm),theory(equality)],[c_221751,c_3013]) ).
tff(c_261610,plain,
! [X1_789,X0_864] : ( join(X1_789,complement(join(X0_864,meet(complement(X0_864),complement(X1_789))))) = complement(complement(X1_789)) ),
inference(superposition,[status(thm),theory(equality)],[c_261599,c_222086]) ).
tff(c_266777,plain,
! [X1_875,X0_876] : ( join(X1_875,meet(complement(X0_876),join(X0_876,X1_875))) = X1_875 ),
inference(demodulation,[status(thm),theory(equality)],[c_29483,c_224133,c_3013,c_261610]) ).
tff(c_267573,plain,
join('#skF_1',meet(complement(complement(composition('#skF_3',converse('#skF_2')))),top)) = '#skF_1',
inference(superposition,[status(thm),theory(equality)],[c_129949,c_266777]) ).
tff(c_268308,plain,
join('#skF_1',composition('#skF_3',converse('#skF_2'))) = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_3543,c_3013,c_267573]) ).
tff(c_268310,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_38,c_268308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : REL044+2 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.14 % 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
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 15:30:07 EDT 2023
% 0.15/0.36 % CPUTime :
% 69.50/55.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 69.50/55.08
% 69.50/55.08 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 69.83/55.12
% 69.83/55.12 Inference rules
% 69.83/55.12 ----------------------
% 69.83/55.12 #Ref : 0
% 69.83/55.12 #Sup : 65875
% 69.83/55.12 #Fact : 0
% 69.83/55.12 #Define : 0
% 69.83/55.12 #Split : 0
% 69.83/55.12 #Chain : 0
% 69.83/55.12 #Close : 0
% 69.83/55.12
% 69.83/55.12 Ordering : KBO
% 69.83/55.12
% 69.83/55.12 Simplification rules
% 69.83/55.12 ----------------------
% 69.83/55.12 #Subsume : 1157
% 69.83/55.12 #Demod : 122914
% 69.83/55.12 #Tautology : 37906
% 69.83/55.12 #SimpNegUnit : 1
% 69.83/55.12 #BackRed : 123
% 69.83/55.12
% 69.83/55.12 #Partial instantiations: 0
% 69.83/55.12 #Strategies tried : 1
% 69.83/55.12
% 69.83/55.12 Timing (in seconds)
% 69.83/55.12 ----------------------
% 69.83/55.13 Preprocessing : 0.50
% 69.83/55.13 Parsing : 0.27
% 69.83/55.13 CNF conversion : 0.03
% 69.83/55.13 Main loop : 53.53
% 69.83/55.13 Inferencing : 3.94
% 69.83/55.13 Reduction : 39.33
% 69.83/55.13 Demodulation : 37.36
% 69.83/55.13 BG Simplification : 0.48
% 69.83/55.13 Subsumption : 7.50
% 69.83/55.13 Abstraction : 0.99
% 69.83/55.13 MUC search : 0.00
% 69.83/55.13 Cooper : 0.00
% 69.83/55.13 Total : 54.11
% 69.83/55.13 Index Insertion : 0.00
% 69.83/55.13 Index Deletion : 0.00
% 69.83/55.13 Index Matching : 0.00
% 69.83/55.13 BG Taut test : 0.00
%------------------------------------------------------------------------------