TSTP Solution File: REL004+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : REL004+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n021.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 10:54:24 EDT 2023
% Result : Theorem 21.27s 11.02s
% Output : CNFRefutation 21.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 24
% Syntax : Number of formulae : 150 ( 141 unt; 9 typ; 0 def)
% Number of atoms : 141 ( 140 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 212 (; 212 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ meet > join > composition > #nlpp > converse > complement > zero > top > one > #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_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/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).
tff(f_69,axiom,
! [X0] : ( converse(converse(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
tff(f_64,axiom,
! [X0] : ( composition(X0,one) = X0 ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
tff(f_53,axiom,
! [X0,X1] : ( join(X0,X1) = join(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
tff(f_75,axiom,
! [X0,X1] : ( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
tff(f_57,axiom,
! [X0,X1] : ( X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
tff(f_78,axiom,
! [X0] : ( top = join(X0,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).
tff(f_55,axiom,
! [X0,X1,X2] : ( join(X0,join(X1,X2)) = join(join(X0,X1),X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
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/sandbox/benchmark/Axioms/REL001+1.ax',dedekind_law) ).
tff(f_118,negated_conjecture,
~ ! [X0] : ( converse(complement(X0)) = complement(converse(X0)) ),
file('/export/starexec/sandbox/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_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_168,plain,
! [X1_43,X0_44] : ( composition(converse(X1_43),converse(X0_44)) = converse(composition(X0_44,X1_43)) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_3078,plain,
! [X0_105,X1_106] : ( converse(composition(converse(X0_105),X1_106)) = composition(converse(X1_106),X0_105) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_168]) ).
tff(c_3154,plain,
! [X0_105] : ( composition(converse(one),X0_105) = converse(converse(X0_105)) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_3078]) ).
tff(c_3172,plain,
! [X0_105] : ( composition(converse(one),X0_105) = X0_105 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_3154]) ).
tff(c_3174,plain,
! [X0_107] : ( composition(converse(one),X0_107) = X0_107 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_3154]) ).
tff(c_358,plain,
! [X0_50,X1_51,X2_52] : ( composition(composition(X0_50,X1_51),X2_52) = composition(X0_50,composition(X1_51,X2_52)) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_380,plain,
! [X0_13,X2_52] : ( composition(X0_13,composition(one,X2_52)) = composition(X0_13,X2_52) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_358]) ).
tff(c_3211,plain,
! [X2_52] : ( composition(converse(one),X2_52) = composition(one,X2_52) ),
inference(superposition,[status(thm),theory(equality)],[c_3174,c_380]) ).
tff(c_3245,plain,
! [X2_52] : ( composition(one,X2_52) = X2_52 ),
inference(demodulation,[status(thm),theory(equality)],[c_3172,c_3211]) ).
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_3222,plain,
converse(one) = one,
inference(superposition,[status(thm),theory(equality)],[c_3174,c_12]) ).
tff(c_3340,plain,
! [X2_109] : ( composition(one,X2_109) = X2_109 ),
inference(demodulation,[status(thm),theory(equality)],[c_3172,c_3211]) ).
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_3363,plain,
! [X2_109] : ( join(composition(converse(one),complement(X2_109)),complement(X2_109)) = complement(X2_109) ),
inference(superposition,[status(thm),theory(equality)],[c_3340,c_22]) ).
tff(c_3394,plain,
! [X2_110] : ( join(complement(X2_110),complement(X2_110)) = complement(X2_110) ),
inference(demodulation,[status(thm),theory(equality)],[c_3245,c_2,c_3222,c_3363]) ).
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_35,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_3403,plain,
! [X2_110] : ( join(meet(X2_110,complement(X2_110)),complement(complement(X2_110))) = X2_110 ),
inference(superposition,[status(thm),theory(equality)],[c_3394,c_35]) ).
tff(c_3643,plain,
! [X2_112] : ( join(zero,complement(complement(X2_112))) = X2_112 ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_3403]) ).
tff(c_24,plain,
! [X0_24] : ( join(X0_24,complement(X0_24)) = top ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_109,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_143,plain,
! [X0_41] : ( meet(X0_41,complement(X0_41)) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_109]) ).
tff(c_146,plain,
complement(top) = zero,
inference(demodulation,[status(thm),theory(equality)],[c_26,c_143]) ).
tff(c_153,plain,
! [X0_8] : ( complement(join(complement(X0_8),zero)) = meet(X0_8,top) ),
inference(superposition,[status(thm),theory(equality)],[c_146,c_8]) ).
tff(c_162,plain,
! [X0_8] : ( complement(join(zero,complement(X0_8))) = meet(X0_8,top) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_153]) ).
tff(c_3661,plain,
! [X2_112] : ( meet(complement(X2_112),top) = complement(X2_112) ),
inference(superposition,[status(thm),theory(equality)],[c_3643,c_162]) ).
tff(c_3382,plain,
! [X2_109] : ( join(complement(X2_109),complement(X2_109)) = complement(X2_109) ),
inference(demodulation,[status(thm),theory(equality)],[c_3245,c_2,c_3222,c_3363]) ).
tff(c_577,plain,
! [X0_59,X1_60,X2_61] : ( join(join(X0_59,X1_60),X2_61) = join(X0_59,join(X1_60,X2_61)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_5062,plain,
! [X0_129,X1_130] : ( join(X0_129,join(X1_130,complement(join(X0_129,X1_130)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_577]) ).
tff(c_5134,plain,
! [X2_109] : ( join(complement(X2_109),join(complement(X2_109),complement(complement(X2_109)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_3382,c_5062]) ).
tff(c_5301,plain,
! [X2_131] : ( join(top,complement(X2_131)) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_24,c_5134]) ).
tff(c_644,plain,
! [X0_59,X1_60] : ( join(X0_59,join(X1_60,complement(join(X0_59,X1_60)))) = top ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_577]) ).
tff(c_5348,plain,
! [X0_132] : ( join(X0_132,top) = top ),
inference(superposition,[status(thm),theory(equality)],[c_5301,c_644]) ).
tff(c_5361,plain,
! [X0_6] : ( join(meet(X0_6,top),complement(top)) = X0_6 ),
inference(superposition,[status(thm),theory(equality)],[c_5348,c_35]) ).
tff(c_5710,plain,
! [X0_136] : ( join(zero,meet(X0_136,top)) = X0_136 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_146,c_5361]) ).
tff(c_6130,plain,
! [X2_141] : ( join(zero,complement(X2_141)) = complement(X2_141) ),
inference(superposition,[status(thm),theory(equality)],[c_3661,c_5710]) ).
tff(c_3453,plain,
! [X2_110] : ( join(zero,complement(complement(X2_110))) = X2_110 ),
inference(demodulation,[status(thm),theory(equality)],[c_26,c_3403]) ).
tff(c_6146,plain,
! [X2_110] : ( complement(complement(X2_110)) = X2_110 ),
inference(superposition,[status(thm),theory(equality)],[c_6130,c_3453]) ).
tff(c_6195,plain,
! [X2_110] : ( join(zero,X2_110) = X2_110 ),
inference(demodulation,[status(thm),theory(equality)],[c_6146,c_3453]) ).
tff(c_302,plain,
! [X0_47,X1_48] : ( join(converse(X0_47),converse(X1_48)) = converse(join(X0_47,X1_48)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_433,plain,
! [X1_55,X0_56] : ( join(converse(X1_55),converse(X0_56)) = converse(join(X0_56,X1_55)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_302]) ).
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_470,plain,
! [X1_57,X0_58] : ( converse(join(X1_57,X0_58)) = converse(join(X0_58,X1_57)) ),
inference(superposition,[status(thm),theory(equality)],[c_433,c_18]) ).
tff(c_521,plain,
! [X1_57,X0_58] : ( converse(converse(join(X1_57,X0_58))) = join(X0_58,X1_57) ),
inference(superposition,[status(thm),theory(equality)],[c_470,c_16]) ).
tff(c_5371,plain,
! [X0_132] : ( join(top,X0_132) = converse(converse(top)) ),
inference(superposition,[status(thm),theory(equality)],[c_5348,c_521]) ).
tff(c_5423,plain,
! [X0_133] : ( join(top,X0_133) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_5371]) ).
tff(c_4117,plain,
! [X0_119,X1_120] : ( converse(join(converse(X0_119),X1_120)) = join(X0_119,converse(X1_120)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_302]) ).
tff(c_4235,plain,
! [X0_119] : ( join(X0_119,converse(complement(converse(X0_119)))) = converse(top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_4117]) ).
tff(c_5440,plain,
converse(top) = top,
inference(superposition,[status(thm),theory(equality)],[c_5423,c_4235]) ).
tff(c_11015,plain,
! [X0_188] : ( join(X0_188,converse(complement(converse(X0_188)))) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_5440,c_4235]) ).
tff(c_11076,plain,
! [X0_6] : ( join(meet(X0_6,converse(complement(converse(complement(X0_6))))),complement(top)) = X0_6 ),
inference(superposition,[status(thm),theory(equality)],[c_11015,c_35]) ).
tff(c_11174,plain,
! [X0_6] : ( meet(X0_6,converse(complement(converse(complement(X0_6))))) = X0_6 ),
inference(demodulation,[status(thm),theory(equality)],[c_6195,c_2,c_146,c_11076]) ).
tff(c_2341,plain,
! [X1_95,X0_96] : ( complement(join(complement(X1_95),complement(X0_96))) = meet(X0_96,X1_95) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_109]) ).
tff(c_2389,plain,
! [X1_95,X0_96] : ( meet(X1_95,X0_96) = meet(X0_96,X1_95) ),
inference(superposition,[status(thm),theory(equality)],[c_2341,c_8]) ).
tff(c_3468,plain,
! [X2_111] : ( meet(X2_111,X2_111) = complement(complement(X2_111)) ),
inference(superposition,[status(thm),theory(equality)],[c_3394,c_8]) ).
tff(c_1025,plain,
! [X0_70,X1_71] : ( join(meet(X0_70,X1_71),complement(join(complement(X0_70),X1_71))) = X0_70 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_6]) ).
tff(c_1091,plain,
! [X0_25] : ( join(zero,complement(join(complement(X0_25),complement(X0_25)))) = X0_25 ),
inference(superposition,[status(thm),theory(equality)],[c_26,c_1025]) ).
tff(c_1104,plain,
! [X0_72] : ( join(zero,meet(X0_72,X0_72)) = X0_72 ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1091]) ).
tff(c_1113,plain,
! [X0_72] : ( join(meet(X0_72,X0_72),zero) = converse(converse(X0_72)) ),
inference(superposition,[status(thm),theory(equality)],[c_1104,c_521]) ).
tff(c_1121,plain,
! [X0_72] : ( join(meet(X0_72,X0_72),zero) = X0_72 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_1113]) ).
tff(c_3526,plain,
! [X2_111] : ( join(complement(complement(X2_111)),zero) = X2_111 ),
inference(superposition,[status(thm),theory(equality)],[c_3468,c_1121]) ).
tff(c_6327,plain,
! [X2_143] : ( join(X2_143,zero) = X2_143 ),
inference(demodulation,[status(thm),theory(equality)],[c_6146,c_3526]) ).
tff(c_323,plain,
! [X0_17,X1_48] : ( converse(join(converse(X0_17),X1_48)) = join(X0_17,converse(X1_48)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_302]) ).
tff(c_6348,plain,
! [X0_17] : ( join(X0_17,converse(zero)) = converse(converse(X0_17)) ),
inference(superposition,[status(thm),theory(equality)],[c_6327,c_323]) ).
tff(c_8278,plain,
! [X0_161] : ( join(X0_161,converse(zero)) = X0_161 ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_6348]) ).
tff(c_8302,plain,
converse(zero) = zero,
inference(superposition,[status(thm),theory(equality)],[c_8278,c_6195]) ).
tff(c_177,plain,
! [X0_44,X0_17] : ( converse(composition(X0_44,converse(X0_17))) = composition(X0_17,converse(X0_44)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_168]) ).
tff(c_22870,plain,
! [X0_288] : ( composition(top,converse(X0_288)) = converse(composition(X0_288,top)) ),
inference(superposition,[status(thm),theory(equality)],[c_5440,c_177]) ).
tff(c_22951,plain,
converse(composition(top,top)) = composition(top,top),
inference(superposition,[status(thm),theory(equality)],[c_5440,c_22870]) ).
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_821,plain,
! [X0_65,X1_66] : ( join(composition(converse(X0_65),complement(composition(X0_65,X1_66))),complement(X1_66)) = complement(X1_66) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_872,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_821]) ).
tff(c_18650,plain,
! [X0_254,X1_255] : ( join(complement(converse(X0_254)),composition(X1_255,complement(converse(composition(X0_254,X1_255))))) = complement(converse(X0_254)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_16,c_872]) ).
tff(c_18731,plain,
! [X1_255] : ( join(complement(top),composition(X1_255,complement(converse(composition(top,X1_255))))) = complement(converse(top)) ),
inference(superposition,[status(thm),theory(equality)],[c_5440,c_18650]) ).
tff(c_18803,plain,
! [X1_255] : ( composition(X1_255,complement(converse(composition(top,X1_255)))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_6195,c_146,c_5440,c_146,c_18731]) ).
tff(c_23016,plain,
composition(top,complement(composition(top,top))) = zero,
inference(superposition,[status(thm),theory(equality)],[c_22951,c_18803]) ).
tff(c_5309,plain,
! [X0_59] : ( join(X0_59,top) = top ),
inference(superposition,[status(thm),theory(equality)],[c_5301,c_644]) ).
tff(c_1167,plain,
! [X0_74,X2_75,X1_76] : ( join(composition(X0_74,X2_75),composition(X1_76,X2_75)) = composition(join(X0_74,X1_76),X2_75) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_1185,plain,
! [X1_76,X2_75,X0_74] : ( join(composition(X1_76,X2_75),composition(X0_74,X2_75)) = composition(join(X0_74,X1_76),X2_75) ),
inference(superposition,[status(thm),theory(equality)],[c_1167,c_2]) ).
tff(c_23181,plain,
! [X0_74] : ( join(zero,composition(X0_74,complement(composition(top,top)))) = composition(join(X0_74,top),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_23016,c_1185]) ).
tff(c_23214,plain,
! [X0_74] : ( composition(X0_74,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_23016,c_6195,c_5309,c_23181]) ).
tff(c_23666,plain,
! [X0_292] : ( composition(X0_292,complement(composition(top,top))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_23016,c_6195,c_5309,c_23181]) ).
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_1200,plain,
! [X0_10,X1_11,X2_12,X1_76] : ( join(composition(X0_10,composition(X1_11,X2_12)),composition(X1_76,X2_12)) = composition(join(composition(X0_10,X1_11),X1_76),X2_12) ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_1167]) ).
tff(c_23680,plain,
! [X0_10,X1_76,X0_292] : ( join(composition(X0_10,zero),composition(X1_76,complement(composition(top,top)))) = composition(join(composition(X0_10,X0_292),X1_76),complement(composition(top,top))) ),
inference(superposition,[status(thm),theory(equality)],[c_23666,c_1200]) ).
tff(c_23827,plain,
! [X0_293] : ( composition(X0_293,zero) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_23214,c_6195,c_2,c_23214,c_23680]) ).
tff(c_180,plain,
! [X0_17,X1_43] : ( converse(composition(converse(X0_17),X1_43)) = composition(converse(X1_43),X0_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_168]) ).
tff(c_23894,plain,
! [X0_17] : ( composition(converse(zero),X0_17) = converse(zero) ),
inference(superposition,[status(thm),theory(equality)],[c_23827,c_180]) ).
tff(c_23948,plain,
! [X0_17] : ( composition(zero,X0_17) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_8302,c_8302,c_23894]) ).
tff(c_887,plain,
! [X0_13] : ( join(composition(converse(X0_13),complement(X0_13)),complement(one)) = complement(one) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_821]) ).
tff(c_7404,plain,
! [X0_156,X0_154,X1_155] : ( join(X0_156,join(X0_154,X1_155)) = join(X0_154,join(X1_155,X0_156)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_577]) ).
tff(c_7769,plain,
! [X0_24,X0_154] : ( join(complement(X0_24),join(X0_154,X0_24)) = join(X0_154,top) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_7404]) ).
tff(c_8880,plain,
! [X0_166,X0_167] : ( join(complement(X0_166),join(X0_167,X0_166)) = top ),
inference(demodulation,[status(thm),theory(equality)],[c_5309,c_7769]) ).
tff(c_8912,plain,
! [X0_166,X0_167] : ( join(meet(X0_166,join(X0_167,X0_166)),complement(top)) = X0_166 ),
inference(superposition,[status(thm),theory(equality)],[c_8880,c_35]) ).
tff(c_9081,plain,
! [X0_168,X0_169] : ( meet(X0_168,join(X0_169,X0_168)) = X0_168 ),
inference(demodulation,[status(thm),theory(equality)],[c_6195,c_2,c_146,c_8912]) ).
tff(c_9209,plain,
! [X1_2,X0_1] : ( meet(X1_2,join(X1_2,X0_1)) = X1_2 ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_9081]) ).
tff(c_1076,plain,
! [X0_8,X1_9] : ( join(meet(X0_8,complement(X1_9)),meet(X0_8,X1_9)) = X0_8 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1025]) ).
tff(c_9884,plain,
! [X0_176,X1_177] : ( join(complement(meet(X0_176,X1_177)),X0_176) = top ),
inference(superposition,[status(thm),theory(equality)],[c_1076,c_8880]) ).
tff(c_139,plain,
! [X1_42,X0_41] : ( complement(join(complement(X1_42),complement(X0_41))) = meet(X0_41,X1_42) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_109]) ).
tff(c_9954,plain,
! [X0_41,X1_177] : ( meet(X0_41,meet(complement(X0_41),X1_177)) = complement(top) ),
inference(superposition,[status(thm),theory(equality)],[c_9884,c_139]) ).
tff(c_10734,plain,
! [X0_184,X1_185] : ( meet(X0_184,meet(complement(X0_184),X1_185)) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_146,c_9954]) ).
tff(c_11440,plain,
! [X0_191,X1_192] : ( meet(X0_191,meet(X1_192,complement(X0_191))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_2389,c_10734]) ).
tff(c_13892,plain,
! [X2_217,X1_218] : ( meet(complement(X2_217),meet(X1_218,X2_217)) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_6146,c_11440]) ).
tff(c_14386,plain,
! [X1_221,X0_222] : ( meet(complement(join(X1_221,X0_222)),X1_221) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_9209,c_13892]) ).
tff(c_14529,plain,
! [X0_13] : ( meet(complement(complement(one)),composition(converse(X0_13),complement(X0_13))) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_887,c_14386]) ).
tff(c_14677,plain,
! [X0_13] : ( meet(one,composition(converse(X0_13),complement(X0_13))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_6146,c_14529]) ).
tff(c_60597,plain,
! [X0_468] : ( meet(one,composition(converse(X0_468),complement(X0_468))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_6146,c_14529]) ).
tff(c_1568,plain,
! [X0_83,X1_84,X2_85] : ( join(meet(composition(X0_83,X1_84),X2_85),composition(meet(X0_83,composition(X2_85,converse(X1_84))),meet(X1_84,composition(converse(X0_83),X2_85)))) = composition(meet(X0_83,composition(X2_85,converse(X1_84))),meet(X1_84,composition(converse(X0_83),X2_85))) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_1647,plain,
! [X0_83,X0_17,X2_85] : ( join(meet(composition(X0_83,converse(X0_17)),X2_85),composition(meet(X0_83,composition(X2_85,X0_17)),meet(converse(X0_17),composition(converse(X0_83),X2_85)))) = composition(meet(X0_83,composition(X2_85,converse(converse(X0_17)))),meet(converse(X0_17),composition(converse(X0_83),X2_85))) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_1568]) ).
tff(c_1664,plain,
! [X0_83,X0_17,X2_85] : ( join(meet(composition(X0_83,converse(X0_17)),X2_85),composition(meet(X0_83,composition(X2_85,X0_17)),meet(converse(X0_17),composition(converse(X0_83),X2_85)))) = composition(meet(X0_83,composition(X2_85,X0_17)),meet(converse(X0_17),composition(converse(X0_83),X2_85))) ),
inference(demodulation,[status(thm),theory(equality)],[c_16,c_1647]) ).
tff(c_60622,plain,
! [X0_468] : ( join(meet(composition(one,converse(complement(X0_468))),converse(X0_468)),composition(zero,meet(converse(complement(X0_468)),composition(converse(one),converse(X0_468))))) = composition(meet(one,composition(converse(X0_468),complement(X0_468))),meet(converse(complement(X0_468)),composition(converse(one),converse(X0_468)))) ),
inference(superposition,[status(thm),theory(equality)],[c_60597,c_1664]) ).
tff(c_60848,plain,
! [X0_469] : ( meet(converse(X0_469),converse(complement(X0_469))) = zero ),
inference(demodulation,[status(thm),theory(equality)],[c_23948,c_14677,c_6195,c_2,c_23948,c_2,c_3245,c_2389,c_2389,c_2389,c_12,c_20,c_2,c_12,c_20,c_60622]) ).
tff(c_62293,plain,
! [X2_473] : ( meet(converse(complement(X2_473)),converse(X2_473)) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_6146,c_60848]) ).
tff(c_62549,plain,
! [X0_474] : ( meet(converse(complement(converse(X0_474))),X0_474) = zero ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_62293]) ).
tff(c_1805,plain,
! [X0_87,X1_88] : ( join(meet(X0_87,complement(X1_88)),meet(X0_87,X1_88)) = X0_87 ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1025]) ).
tff(c_1826,plain,
! [X0_87,X1_88] : ( join(meet(X0_87,X1_88),meet(X0_87,complement(X1_88))) = X0_87 ),
inference(superposition,[status(thm),theory(equality)],[c_1805,c_2]) ).
tff(c_62558,plain,
! [X1_88] : ( join(meet(converse(complement(converse(complement(X1_88)))),X1_88),zero) = converse(complement(converse(complement(X1_88)))) ),
inference(superposition,[status(thm),theory(equality)],[c_62549,c_1826]) ).
tff(c_62951,plain,
! [X1_475] : ( converse(complement(converse(complement(X1_475)))) = X1_475 ),
inference(demodulation,[status(thm),theory(equality)],[c_11174,c_6195,c_2,c_2389,c_62558]) ).
tff(c_63305,plain,
! [X1_476] : ( complement(converse(complement(X1_476))) = converse(X1_476) ),
inference(superposition,[status(thm),theory(equality)],[c_62951,c_16]) ).
tff(c_63479,plain,
! [X1_476] : ( converse(complement(X1_476)) = complement(converse(X1_476)) ),
inference(superposition,[status(thm),theory(equality)],[c_63305,c_6146]) ).
tff(c_34,plain,
converse(complement('#skF_1')) != complement(converse('#skF_1')),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_64267,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_63479,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : REL004+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 15:32:51 EDT 2023
% 0.14/0.35 % CPUTime :
% 21.27/11.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.38/11.04
% 21.38/11.04 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.58/11.08
% 21.58/11.08 Inference rules
% 21.58/11.08 ----------------------
% 21.58/11.08 #Ref : 0
% 21.58/11.08 #Sup : 15870
% 21.58/11.08 #Fact : 0
% 21.58/11.08 #Define : 0
% 21.58/11.08 #Split : 0
% 21.58/11.08 #Chain : 0
% 21.58/11.08 #Close : 0
% 21.58/11.08
% 21.58/11.08 Ordering : KBO
% 21.58/11.08
% 21.58/11.08 Simplification rules
% 21.58/11.08 ----------------------
% 21.58/11.08 #Subsume : 185
% 21.58/11.08 #Demod : 30014
% 21.58/11.08 #Tautology : 9441
% 21.58/11.08 #SimpNegUnit : 0
% 21.58/11.08 #BackRed : 90
% 21.58/11.08
% 21.58/11.08 #Partial instantiations: 0
% 21.58/11.08 #Strategies tried : 1
% 21.58/11.08
% 21.58/11.08 Timing (in seconds)
% 21.58/11.08 ----------------------
% 21.58/11.09 Preprocessing : 0.51
% 21.58/11.09 Parsing : 0.27
% 21.58/11.09 CNF conversion : 0.03
% 21.58/11.09 Main loop : 9.50
% 21.58/11.09 Inferencing : 1.39
% 21.58/11.09 Reduction : 6.41
% 21.58/11.09 Demodulation : 5.98
% 21.58/11.09 BG Simplification : 0.17
% 21.58/11.09 Subsumption : 1.12
% 21.58/11.09 Abstraction : 0.38
% 21.58/11.09 MUC search : 0.00
% 21.58/11.09 Cooper : 0.00
% 21.58/11.09 Total : 10.08
% 21.58/11.09 Index Insertion : 0.00
% 21.58/11.09 Index Deletion : 0.00
% 21.58/11.09 Index Matching : 0.00
% 21.58/11.09 BG Taut test : 0.00
%------------------------------------------------------------------------------