%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP187-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:38:56 PM UTC 2026
% Result : Unsatisfiable 89.78s 13.56s
% Output : CNFRefutation 89.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 16
% Syntax : Number of clauses : 330 ( 330 unt; 0 nHn; 116 RR)
% Number of literals : 330 ( 329 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 408 ( 66 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(p33_1,hypothesis,
greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b))) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33_1) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(prove_p33,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p33) ).
cnf(c_0_16,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_17,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_18,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_19,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_20,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_21,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_22,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_24,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_25,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).
cnf(c_0_26,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_27,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_28,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_24]) ).
cnf(c_0_29,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_30,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = X3,
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_31,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_32,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
associativity_of_lub ).
cnf(c_0_34,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
associativity_of_glb ).
cnf(c_0_35,plain,
multiply(X1,greatest_lower_bound(identity,inverse(X1))) = greatest_lower_bound(X1,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_24]) ).
cnf(c_0_36,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld ).
cnf(c_0_37,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_29]),c_0_22]) ).
cnf(c_0_38,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_39,plain,
greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X2,X1),X3)) = greatest_lower_bound(X1,X3),
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_41,hypothesis,
greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b))) = identity,
p33_1 ).
cnf(c_0_42,plain,
multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_25]),c_0_24]) ).
cnf(c_0_43,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
cnf(c_0_44,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_45,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_46,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_37]),c_0_25]) ).
cnf(c_0_47,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_34]) ).
cnf(c_0_48,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X3,X1))) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_31]),c_0_34]) ).
cnf(c_0_49,hypothesis,
greatest_lower_bound(inverse(a),least_upper_bound(b,inverse(b))) = greatest_lower_bound(identity,inverse(a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_24]) ).
cnf(c_0_50,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X3,greatest_lower_bound(X1,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_51,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_24]),c_0_34]) ).
cnf(c_0_52,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_17]) ).
cnf(c_0_53,plain,
greatest_lower_bound(identity,multiply(X1,inverse(X2))) = multiply(greatest_lower_bound(X1,X2),inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_29]),c_0_24]) ).
cnf(c_0_54,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_24]) ).
cnf(c_0_56,hypothesis,
greatest_lower_bound(identity,greatest_lower_bound(inverse(a),inverse(b))) = greatest_lower_bound(inverse(a),inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_24]),c_0_51]),c_0_24]) ).
cnf(c_0_57,plain,
multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_58,plain,
greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_59,hypothesis,
least_upper_bound(identity,greatest_lower_bound(X1,greatest_lower_bound(inverse(a),inverse(b)))) = identity,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_22]),c_0_22]) ).
cnf(c_0_61,hypothesis,
least_upper_bound(identity,greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),X1))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_24]),c_0_34]) ).
cnf(c_0_62,plain,
greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(least_upper_bound(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_26]),c_0_24]) ).
cnf(c_0_63,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_64,hypothesis,
least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(least_upper_bound(b,X1)))) = identity,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,plain,
greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(least_upper_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_32]),c_0_24]) ).
cnf(c_0_66,plain,
greatest_lower_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = greatest_lower_bound(X1,X3),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_67,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_31]),c_0_34]) ).
cnf(c_0_68,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_69,plain,
least_upper_bound(identity,multiply(X1,inverse(X2))) = multiply(least_upper_bound(X1,X2),inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_29]),c_0_27]) ).
cnf(c_0_70,hypothesis,
least_upper_bound(identity,inverse(least_upper_bound(a,b))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_27]) ).
cnf(c_0_71,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_27]),c_0_33]) ).
cnf(c_0_72,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,X3))) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_66]) ).
cnf(c_0_73,hypothesis,
greatest_lower_bound(a,least_upper_bound(b,inverse(b))) = greatest_lower_bound(a,identity),
inference(spm,[status(thm)],[c_0_66,c_0_41]) ).
cnf(c_0_74,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_22]),c_0_27]) ).
cnf(c_0_75,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_18]),c_0_27]) ).
cnf(c_0_76,plain,
greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X3,least_upper_bound(X4,X1)))) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_77,hypothesis,
least_upper_bound(a,least_upper_bound(b,identity)) = least_upper_bound(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_25]),c_0_18]),c_0_25]),c_0_18]),c_0_71]),c_0_27]) ).
cnf(c_0_78,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,greatest_lower_bound(X2,X3))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_34]) ).
cnf(c_0_79,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(b,identity)) = greatest_lower_bound(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_51]),c_0_24]) ).
cnf(c_0_80,hypothesis,
greatest_lower_bound(least_upper_bound(a,inverse(a)),greatest_lower_bound(least_upper_bound(b,inverse(b)),X1)) = greatest_lower_bound(identity,X1),
inference(spm,[status(thm)],[c_0_34,c_0_41]) ).
cnf(c_0_81,plain,
multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_68,c_0_19]) ).
cnf(c_0_82,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X1,X2),inverse(X2))) = identity,
inference(spm,[status(thm)],[c_0_31,c_0_53]) ).
cnf(c_0_83,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_19]) ).
cnf(c_0_84,plain,
multiply(X1,multiply(inverse(multiply(X2,X1)),X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_16,c_0_46]) ).
cnf(c_0_85,plain,
multiply(least_upper_bound(X1,identity),X1) = multiply(X1,least_upper_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_86,plain,
least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X2,X1),X3)) = least_upper_bound(X1,X3),
inference(spm,[status(thm)],[c_0_33,c_0_38]) ).
cnf(c_0_87,plain,
multiply(inverse(X1),greatest_lower_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_17]),c_0_24]) ).
cnf(c_0_88,hypothesis,
greatest_lower_bound(identity,least_upper_bound(X1,least_upper_bound(a,b))) = identity,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_89,plain,
greatest_lower_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),greatest_lower_bound(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_90,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,greatest_lower_bound(X3,X2))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_24]) ).
cnf(c_0_91,hypothesis,
least_upper_bound(greatest_lower_bound(a,b),greatest_lower_bound(b,identity)) = greatest_lower_bound(b,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_79]),c_0_27]) ).
cnf(c_0_92,hypothesis,
greatest_lower_bound(identity,least_upper_bound(b,least_upper_bound(inverse(b),X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_26]),c_0_41]),c_0_33]) ).
cnf(c_0_93,plain,
least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) = inverse(greatest_lower_bound(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_22]),c_0_22]),c_0_27]) ).
cnf(c_0_94,plain,
greatest_lower_bound(inverse(X1),inverse(multiply(X2,X1))) = multiply(inverse(X1),greatest_lower_bound(identity,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_83]),c_0_24]) ).
cnf(c_0_95,plain,
multiply(X1,multiply(inverse(multiply(X1,least_upper_bound(X1,identity))),X2)) = multiply(inverse(least_upper_bound(X1,identity)),X2),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_96,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(greatest_lower_bound(X3,X1),X2)) = least_upper_bound(greatest_lower_bound(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_86]),c_0_24]) ).
cnf(c_0_97,plain,
least_upper_bound(greatest_lower_bound(X1,identity),greatest_lower_bound(identity,inverse(X1))) = multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_87]),c_0_27]) ).
cnf(c_0_98,plain,
greatest_lower_bound(X1,multiply(least_upper_bound(X1,X2),greatest_lower_bound(X3,identity))) = greatest_lower_bound(X1,multiply(least_upper_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_66,c_0_28]) ).
cnf(c_0_99,plain,
multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_17]),c_0_27]) ).
cnf(c_0_100,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,least_upper_bound(X2,X3))) = least_upper_bound(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_33]) ).
cnf(c_0_101,hypothesis,
least_upper_bound(b,least_upper_bound(identity,inverse(b))) = least_upper_bound(b,inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_41]),c_0_33]),c_0_27]) ).
cnf(c_0_102,hypothesis,
greatest_lower_bound(identity,least_upper_bound(a,least_upper_bound(b,X1))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_27]),c_0_33]) ).
cnf(c_0_103,plain,
greatest_lower_bound(identity,multiply(inverse(X1),least_upper_bound(X1,X2))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_26]),c_0_17]) ).
cnf(c_0_104,hypothesis,
least_upper_bound(greatest_lower_bound(a,b),greatest_lower_bound(a,identity)) = greatest_lower_bound(a,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_79]),c_0_27]) ).
cnf(c_0_105,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_18]),c_0_24]) ).
cnf(c_0_106,plain,
greatest_lower_bound(identity,multiply(inverse(X1),least_upper_bound(X2,X1))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_32]),c_0_17]) ).
cnf(c_0_107,hypothesis,
least_upper_bound(identity,multiply(greatest_lower_bound(a,b),inverse(greatest_lower_bound(b,identity)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_91]),c_0_29]) ).
cnf(c_0_108,hypothesis,
greatest_lower_bound(identity,least_upper_bound(b,inverse(greatest_lower_bound(X1,b)))) = identity,
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_109,plain,
multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_23,c_0_45]) ).
cnf(c_0_110,plain,
multiply(inverse(X1),greatest_lower_bound(identity,inverse(X2))) = multiply(inverse(multiply(X2,X1)),greatest_lower_bound(X2,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_37]),c_0_24]),c_0_94]) ).
cnf(c_0_111,plain,
multiply(X1,greatest_lower_bound(X2,inverse(X1))) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_29]),c_0_24]) ).
cnf(c_0_112,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_37,c_0_45]) ).
cnf(c_0_113,plain,
multiply(inverse(X1),least_upper_bound(X1,identity)) = least_upper_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_17]),c_0_27]) ).
cnf(c_0_114,plain,
multiply(inverse(least_upper_bound(X1,identity)),X1) = multiply(X1,inverse(least_upper_bound(X1,identity))),
inference(spm,[status(thm)],[c_0_95,c_0_37]) ).
cnf(c_0_115,plain,
multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_31]),c_0_98]),c_0_99]),c_0_18]),c_0_26]) ).
cnf(c_0_116,hypothesis,
greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(b,inverse(b))) = least_upper_bound(b,identity),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_117,hypothesis,
greatest_lower_bound(identity,least_upper_bound(a,multiply(b,least_upper_bound(X1,identity)))) = identity,
inference(spm,[status(thm)],[c_0_102,c_0_74]) ).
cnf(c_0_118,plain,
least_upper_bound(multiply(X1,X2),greatest_lower_bound(X3,multiply(X1,greatest_lower_bound(X2,identity)))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_47,c_0_28]) ).
cnf(c_0_119,hypothesis,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(a,b)),greatest_lower_bound(a,identity))) = identity,
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_120,plain,
least_upper_bound(multiply(X1,X2),greatest_lower_bound(X3,multiply(greatest_lower_bound(X1,identity),X2))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_47,c_0_105]) ).
cnf(c_0_121,hypothesis,
greatest_lower_bound(identity,multiply(greatest_lower_bound(b,identity),inverse(greatest_lower_bound(a,b)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_54]),c_0_22]) ).
cnf(c_0_122,hypothesis,
greatest_lower_bound(identity,least_upper_bound(b,inverse(greatest_lower_bound(b,X1)))) = identity,
inference(spm,[status(thm)],[c_0_108,c_0_24]) ).
cnf(c_0_123,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_58]),c_0_22]),c_0_22]) ).
cnf(c_0_124,plain,
multiply(inverse(greatest_lower_bound(identity,X1)),greatest_lower_bound(X1,identity)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_110]),c_0_111]),c_0_22]) ).
cnf(c_0_125,plain,
greatest_lower_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),greatest_lower_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_17]),c_0_24]) ).
cnf(c_0_126,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_26]),c_0_33]) ).
cnf(c_0_127,plain,
multiply(greatest_lower_bound(inverse(X1),X2),X1) = greatest_lower_bound(identity,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_44,c_0_17]) ).
cnf(c_0_128,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_17]),c_0_24]) ).
cnf(c_0_129,plain,
inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(X1,identity))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]) ).
cnf(c_0_130,plain,
inverse(least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(X1,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_115]),c_0_22]) ).
cnf(c_0_131,hypothesis,
greatest_lower_bound(least_upper_bound(b,identity),greatest_lower_bound(X1,least_upper_bound(b,inverse(b)))) = greatest_lower_bound(X1,least_upper_bound(b,identity)),
inference(spm,[status(thm)],[c_0_51,c_0_116]) ).
cnf(c_0_132,hypothesis,
greatest_lower_bound(identity,least_upper_bound(a,multiply(b,least_upper_bound(identity,X1)))) = identity,
inference(spm,[status(thm)],[c_0_117,c_0_27]) ).
cnf(c_0_133,hypothesis,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,b)),a)) = multiply(inverse(greatest_lower_bound(a,b)),a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_27]) ).
cnf(c_0_134,plain,
least_upper_bound(X1,multiply(X2,multiply(X3,X1))) = multiply(least_upper_bound(identity,multiply(X2,X3)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_16]),c_0_27]) ).
cnf(c_0_135,hypothesis,
least_upper_bound(identity,multiply(b,inverse(greatest_lower_bound(a,b)))) = multiply(b,inverse(greatest_lower_bound(a,b))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_27]) ).
cnf(c_0_136,hypothesis,
least_upper_bound(identity,inverse(least_upper_bound(b,inverse(greatest_lower_bound(b,X1))))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_122]),c_0_18]) ).
cnf(c_0_137,plain,
least_upper_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = inverse(greatest_lower_bound(X2,inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_123]),c_0_27]) ).
cnf(c_0_138,plain,
multiply(inverse(greatest_lower_bound(X1,X2)),greatest_lower_bound(X2,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_112]),c_0_24]),c_0_16]),c_0_109]),c_0_22]) ).
cnf(c_0_139,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X2,X1)) = least_upper_bound(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_126]) ).
cnf(c_0_140,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(b,greatest_lower_bound(identity,X1))) = greatest_lower_bound(a,greatest_lower_bound(b,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_79]),c_0_34]),c_0_34]) ).
cnf(c_0_141,hypothesis,
greatest_lower_bound(identity,multiply(least_upper_bound(b,inverse(b)),a)) = greatest_lower_bound(a,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_49]),c_0_128]),c_0_18]),c_0_24]) ).
cnf(c_0_142,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_143,plain,
multiply(X1,inverse(least_upper_bound(X1,identity))) = greatest_lower_bound(X1,identity),
inference(rw,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_144,plain,
multiply(X1,greatest_lower_bound(inverse(multiply(X2,X1)),X3)) = greatest_lower_bound(inverse(X2),multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_46]) ).
cnf(c_0_145,plain,
multiply(least_upper_bound(inverse(multiply(X1,X2)),X3),X1) = least_upper_bound(inverse(X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_63,c_0_37]) ).
cnf(c_0_146,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(identity,inverse(b))) = greatest_lower_bound(a,inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_73]),c_0_24]),c_0_34]),c_0_24]) ).
cnf(c_0_147,plain,
greatest_lower_bound(identity,inverse(X1)) = inverse(least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_25]),c_0_24]) ).
cnf(c_0_148,hypothesis,
greatest_lower_bound(least_upper_bound(b,identity),least_upper_bound(a,inverse(a))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_41]),c_0_24]),c_0_32]),c_0_24]) ).
cnf(c_0_149,hypothesis,
greatest_lower_bound(identity,multiply(b,multiply(inverse(greatest_lower_bound(a,b)),a))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_134]),c_0_135]),c_0_16]) ).
cnf(c_0_150,hypothesis,
least_upper_bound(identity,greatest_lower_bound(b,inverse(b))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_25]) ).
cnf(c_0_151,plain,
greatest_lower_bound(least_upper_bound(X1,identity),least_upper_bound(identity,inverse(X1))) = multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_113]),c_0_24]) ).
cnf(c_0_152,plain,
multiply(inverse(least_upper_bound(X1,X2)),least_upper_bound(X2,X1)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_139]) ).
cnf(c_0_153,hypothesis,
least_upper_bound(identity,greatest_lower_bound(a,b)) = identity,
inference(spm,[status(thm)],[c_0_47,c_0_79]) ).
cnf(c_0_154,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(b,multiply(least_upper_bound(b,inverse(b)),a))) = greatest_lower_bound(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_51]),c_0_79]),c_0_43]) ).
cnf(c_0_155,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_142]) ).
cnf(c_0_156,plain,
inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_143]),c_0_144]),c_0_22]),c_0_83]),c_0_145]),c_0_18]) ).
cnf(c_0_157,hypothesis,
least_upper_bound(identity,greatest_lower_bound(a,inverse(b))) = identity,
inference(spm,[status(thm)],[c_0_55,c_0_146]) ).
cnf(c_0_158,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(least_upper_bound(identity,X1)),X2),
inference(spm,[status(thm)],[c_0_34,c_0_147]) ).
cnf(c_0_159,hypothesis,
greatest_lower_bound(least_upper_bound(b,identity),inverse(a)) = inverse(least_upper_bound(a,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_148]),c_0_24]),c_0_147]),c_0_27]),c_0_24]) ).
cnf(c_0_160,plain,
multiply(inverse(least_upper_bound(X1,identity)),X1) = greatest_lower_bound(X1,identity),
inference(rw,[status(thm)],[c_0_114,c_0_143]) ).
cnf(c_0_161,hypothesis,
greatest_lower_bound(inverse(b),multiply(inverse(greatest_lower_bound(a,b)),a)) = inverse(b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_149]),c_0_22]),c_0_22]) ).
cnf(c_0_162,hypothesis,
greatest_lower_bound(b,greatest_lower_bound(identity,inverse(b))) = greatest_lower_bound(b,inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_150]),c_0_34]),c_0_24]) ).
cnf(c_0_163,plain,
greatest_lower_bound(least_upper_bound(X1,identity),least_upper_bound(identity,inverse(X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_147]),c_0_152]) ).
cnf(c_0_164,hypothesis,
least_upper_bound(identity,least_upper_bound(greatest_lower_bound(a,b),X1)) = least_upper_bound(identity,X1),
inference(spm,[status(thm)],[c_0_33,c_0_153]) ).
cnf(c_0_165,hypothesis,
least_upper_bound(greatest_lower_bound(a,b),multiply(least_upper_bound(b,inverse(b)),a)) = multiply(least_upper_bound(b,inverse(b)),a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_154]),c_0_27]) ).
cnf(c_0_166,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_155]) ).
cnf(c_0_167,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(spm,[status(thm)],[c_0_30,c_0_45]) ).
cnf(c_0_168,plain,
multiply(least_upper_bound(X1,identity),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_29]),c_0_27]) ).
cnf(c_0_169,plain,
inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_156,c_0_27]) ).
cnf(c_0_170,plain,
greatest_lower_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,identity))) = multiply(inverse(X1),greatest_lower_bound(X2,greatest_lower_bound(X1,identity))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_87]),c_0_50]),c_0_24]),c_0_51]),c_0_28]) ).
cnf(c_0_171,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(inverse(least_upper_bound(b,identity)),X1)) = greatest_lower_bound(a,greatest_lower_bound(inverse(b),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_157]),c_0_34]),c_0_34]),c_0_51]),c_0_158]),c_0_27]) ).
cnf(c_0_172,plain,
greatest_lower_bound(X1,multiply(least_upper_bound(X2,X1),greatest_lower_bound(X3,identity))) = greatest_lower_bound(X1,multiply(least_upper_bound(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_173,hypothesis,
greatest_lower_bound(identity,multiply(least_upper_bound(b,identity),a)) = greatest_lower_bound(a,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_159]),c_0_25]),c_0_25]),c_0_160]) ).
cnf(c_0_174,hypothesis,
greatest_lower_bound(a,inverse(least_upper_bound(b,identity))) = greatest_lower_bound(a,inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147]),c_0_27]) ).
cnf(c_0_175,hypothesis,
greatest_lower_bound(b,multiply(inverse(a),greatest_lower_bound(a,b))) = multiply(inverse(a),greatest_lower_bound(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_161]),c_0_112]),c_0_25]),c_0_112]),c_0_24]) ).
cnf(c_0_176,hypothesis,
greatest_lower_bound(b,inverse(least_upper_bound(b,identity))) = greatest_lower_bound(b,inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_147]),c_0_27]) ).
cnf(c_0_177,plain,
inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_156]) ).
cnf(c_0_178,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_26]),c_0_22]) ).
cnf(c_0_179,plain,
greatest_lower_bound(X1,least_upper_bound(identity,inverse(X1))) = greatest_lower_bound(X1,identity),
inference(spm,[status(thm)],[c_0_66,c_0_163]) ).
cnf(c_0_180,hypothesis,
least_upper_bound(identity,greatest_lower_bound(a,greatest_lower_bound(b,X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_31]),c_0_153]),c_0_34]) ).
cnf(c_0_181,hypothesis,
least_upper_bound(identity,greatest_lower_bound(X1,greatest_lower_bound(a,b))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_38]),c_0_153]) ).
cnf(c_0_182,hypothesis,
least_upper_bound(a,multiply(inverse(least_upper_bound(b,inverse(b))),greatest_lower_bound(a,b))) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_165]),c_0_19]),c_0_27]) ).
cnf(c_0_183,plain,
inverse(greatest_lower_bound(X1,identity)) = least_upper_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_115]),c_0_166]),c_0_18]) ).
cnf(c_0_184,plain,
multiply(greatest_lower_bound(X1,identity),X1) = multiply(X1,greatest_lower_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_28,c_0_105]) ).
cnf(c_0_185,plain,
multiply(greatest_lower_bound(identity,X1),multiply(least_upper_bound(X1,identity),X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_25]),c_0_169]),c_0_166]) ).
cnf(c_0_186,hypothesis,
multiply(least_upper_bound(b,identity),greatest_lower_bound(a,inverse(b))) = greatest_lower_bound(a,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_25]),c_0_172]),c_0_173]),c_0_25]),c_0_24]),c_0_147]),c_0_27]),c_0_174]) ).
cnf(c_0_187,hypothesis,
least_upper_bound(b,greatest_lower_bound(X1,multiply(inverse(a),greatest_lower_bound(a,b)))) = b,
inference(spm,[status(thm)],[c_0_55,c_0_175]) ).
cnf(c_0_188,hypothesis,
multiply(least_upper_bound(b,inverse(b)),greatest_lower_bound(b,inverse(b))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_176]),c_0_177]),c_0_27]),c_0_33]),c_0_101]) ).
cnf(c_0_189,plain,
greatest_lower_bound(identity,multiply(X1,inverse(X2))) = multiply(greatest_lower_bound(X2,X1),inverse(X2)),
inference(spm,[status(thm)],[c_0_44,c_0_29]) ).
cnf(c_0_190,plain,
least_upper_bound(identity,greatest_lower_bound(X1,inverse(least_upper_bound(identity,X2)))) = identity,
inference(spm,[status(thm)],[c_0_55,c_0_178]) ).
cnf(c_0_191,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(identity,X1))) = greatest_lower_bound(X1,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_179]),c_0_24]),c_0_34]),c_0_147]),c_0_24]) ).
cnf(c_0_192,hypothesis,
least_upper_bound(identity,greatest_lower_bound(a,multiply(greatest_lower_bound(X1,identity),b))) = identity,
inference(spm,[status(thm)],[c_0_180,c_0_105]) ).
cnf(c_0_193,hypothesis,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X1,greatest_lower_bound(a,b)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_181]),c_0_22]) ).
cnf(c_0_194,hypothesis,
greatest_lower_bound(inverse(a),multiply(inverse(greatest_lower_bound(a,b)),least_upper_bound(b,inverse(b)))) = inverse(a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_182]),c_0_112]),c_0_24]) ).
cnf(c_0_195,plain,
inverse(greatest_lower_bound(identity,X1)) = least_upper_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_183,c_0_24]) ).
cnf(c_0_196,plain,
least_upper_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),X3)) = least_upper_bound(X1,X3),
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_197,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X1,identity),X2),multiply(X1,greatest_lower_bound(X1,identity))) = multiply(greatest_lower_bound(X1,identity),greatest_lower_bound(X2,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_184]) ).
cnf(c_0_198,hypothesis,
multiply(greatest_lower_bound(b,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,multiply(b,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_24]),c_0_111]) ).
cnf(c_0_199,hypothesis,
least_upper_bound(b,multiply(inverse(a),greatest_lower_bound(X1,greatest_lower_bound(a,b)))) = b,
inference(spm,[status(thm)],[c_0_187,c_0_23]) ).
cnf(c_0_200,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_85,c_0_27]) ).
cnf(c_0_201,hypothesis,
multiply(least_upper_bound(b,inverse(b)),multiply(greatest_lower_bound(b,inverse(b)),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_188]),c_0_18]) ).
cnf(c_0_202,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X1,X2),inverse(X2))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_32]),c_0_29]) ).
cnf(c_0_203,plain,
least_upper_bound(identity,greatest_lower_bound(X1,inverse(X1))) = identity,
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_204,plain,
inverse(greatest_lower_bound(X1,inverse(X2))) = least_upper_bound(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_177,c_0_24]) ).
cnf(c_0_205,hypothesis,
least_upper_bound(identity,greatest_lower_bound(a,multiply(greatest_lower_bound(identity,X1),b))) = identity,
inference(spm,[status(thm)],[c_0_192,c_0_24]) ).
cnf(c_0_206,hypothesis,
greatest_lower_bound(identity,greatest_lower_bound(X1,greatest_lower_bound(a,b))) = greatest_lower_bound(X1,greatest_lower_bound(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_193]),c_0_25]),c_0_18]),c_0_25]),c_0_18]) ).
cnf(c_0_207,plain,
inverse(greatest_lower_bound(multiply(inverse(X1),X2),X3)) = multiply(inverse(greatest_lower_bound(X2,multiply(X1,X3))),X1),
inference(spm,[status(thm)],[c_0_112,c_0_57]) ).
cnf(c_0_208,hypothesis,
greatest_lower_bound(least_upper_bound(b,inverse(b)),multiply(greatest_lower_bound(a,b),inverse(a))) = multiply(greatest_lower_bound(a,b),inverse(a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_194]),c_0_25]),c_0_25]),c_0_24]) ).
cnf(c_0_209,plain,
multiply(X1,inverse(greatest_lower_bound(X1,X2))) = least_upper_bound(identity,multiply(X1,inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_189]),c_0_54]),c_0_54]) ).
cnf(c_0_210,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_67]) ).
cnf(c_0_211,plain,
least_upper_bound(X1,multiply(least_upper_bound(X2,identity),greatest_lower_bound(X1,X3))) = least_upper_bound(X1,multiply(X2,greatest_lower_bound(X1,X3))),
inference(spm,[status(thm)],[c_0_196,c_0_75]) ).
cnf(c_0_212,plain,
multiply(X1,inverse(greatest_lower_bound(X2,X1))) = least_upper_bound(identity,multiply(X1,inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_53]),c_0_54]),c_0_54]) ).
cnf(c_0_213,hypothesis,
greatest_lower_bound(identity,multiply(b,greatest_lower_bound(a,b))) = multiply(greatest_lower_bound(b,identity),greatest_lower_bound(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_34]),c_0_23]),c_0_79]),c_0_34]),c_0_24]),c_0_79]) ).
cnf(c_0_214,plain,
multiply(X1,least_upper_bound(X2,inverse(X1))) = least_upper_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_29]),c_0_27]) ).
cnf(c_0_215,hypothesis,
least_upper_bound(multiply(a,b),greatest_lower_bound(X1,greatest_lower_bound(a,b))) = multiply(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_199]),c_0_25]),c_0_25]) ).
cnf(c_0_216,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X2,least_upper_bound(identity,X2))) = multiply(greatest_lower_bound(X1,least_upper_bound(identity,X2)),X2),
inference(spm,[status(thm)],[c_0_44,c_0_200]) ).
cnf(c_0_217,hypothesis,
multiply(least_upper_bound(b,inverse(b)),greatest_lower_bound(identity,multiply(b,b))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_53]),c_0_25]),c_0_25]) ).
cnf(c_0_218,plain,
greatest_lower_bound(identity,least_upper_bound(X1,inverse(X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_204]),c_0_18]),c_0_27]) ).
cnf(c_0_219,hypothesis,
least_upper_bound(identity,greatest_lower_bound(a,multiply(greatest_lower_bound(X1,greatest_lower_bound(a,b)),b))) = identity,
inference(spm,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_220,plain,
least_upper_bound(multiply(X1,X2),multiply(X2,least_upper_bound(X2,identity))) = multiply(least_upper_bound(X1,least_upper_bound(X2,identity)),X2),
inference(spm,[status(thm)],[c_0_63,c_0_85]) ).
cnf(c_0_221,hypothesis,
multiply(least_upper_bound(a,b),multiply(inverse(b),greatest_lower_bound(a,b))) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_208]),c_0_24]),c_0_194]),c_0_25]),c_0_54]),c_0_209]),c_0_69]),c_0_16]) ).
cnf(c_0_222,plain,
least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = identity,
inference(spm,[status(thm)],[c_0_31,c_0_125]) ).
cnf(c_0_223,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X3,greatest_lower_bound(X2,X1)))) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_210]),c_0_34]) ).
cnf(c_0_224,hypothesis,
least_upper_bound(a,greatest_lower_bound(identity,multiply(b,a))) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_186]),c_0_31]),c_0_111]) ).
cnf(c_0_225,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X3,X1))) = greatest_lower_bound(X2,multiply(greatest_lower_bound(X3,identity),X1)),
inference(spm,[status(thm)],[c_0_51,c_0_105]) ).
cnf(c_0_226,hypothesis,
least_upper_bound(identity,multiply(b,greatest_lower_bound(a,b))) = least_upper_bound(b,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_16]),c_0_46]),c_0_183]),c_0_214]),c_0_22]),c_0_27]),c_0_166]),c_0_22]) ).
cnf(c_0_227,hypothesis,
least_upper_bound(multiply(a,b),greatest_lower_bound(a,greatest_lower_bound(b,X1))) = multiply(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_24]),c_0_34]) ).
cnf(c_0_228,hypothesis,
greatest_lower_bound(b,greatest_lower_bound(identity,multiply(b,b))) = greatest_lower_bound(identity,multiply(b,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_217]),c_0_31]),c_0_22]),c_0_31]),c_0_24]),c_0_218]),c_0_18]) ).
cnf(c_0_229,hypothesis,
least_upper_bound(identity,greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),b))) = identity,
inference(spm,[status(thm)],[c_0_219,c_0_36]) ).
cnf(c_0_230,hypothesis,
least_upper_bound(a,multiply(inverse(b),greatest_lower_bound(a,b))) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_27]),c_0_222]),c_0_22]),c_0_27]),c_0_222]),c_0_33]),c_0_77]),c_0_221]) ).
cnf(c_0_231,hypothesis,
greatest_lower_bound(b,greatest_lower_bound(identity,multiply(b,a))) = greatest_lower_bound(identity,multiply(b,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_198]),c_0_34]),c_0_43]),c_0_34]),c_0_36]),c_0_198]) ).
cnf(c_0_232,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(identity,multiply(b,a))) = greatest_lower_bound(identity,multiply(b,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_24]),c_0_24]),c_0_50]),c_0_24]),c_0_105]),c_0_225]) ).
cnf(c_0_233,hypothesis,
least_upper_bound(greatest_lower_bound(a,b),inverse(b)) = least_upper_bound(identity,inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_226]),c_0_113]),c_0_22]),c_0_27]) ).
cnf(c_0_234,hypothesis,
least_upper_bound(multiply(a,b),greatest_lower_bound(a,greatest_lower_bound(identity,multiply(b,b)))) = multiply(a,b),
inference(spm,[status(thm)],[c_0_227,c_0_228]) ).
cnf(c_0_235,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(identity,multiply(greatest_lower_bound(a,b),b))) = greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_229]),c_0_34]),c_0_24]) ).
cnf(c_0_236,hypothesis,
greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),inverse(b))) = multiply(greatest_lower_bound(a,b),inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_161]),c_0_25]),c_0_25]),c_0_24]) ).
cnf(c_0_237,hypothesis,
least_upper_bound(multiply(b,a),greatest_lower_bound(a,b)) = multiply(b,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_230]),c_0_25]),c_0_25]) ).
cnf(c_0_238,hypothesis,
greatest_lower_bound(a,multiply(b,greatest_lower_bound(a,identity))) = greatest_lower_bound(identity,multiply(b,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_231]),c_0_232]),c_0_28]) ).
cnf(c_0_239,hypothesis,
greatest_lower_bound(b,inverse(greatest_lower_bound(a,b))) = greatest_lower_bound(b,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_233]),c_0_169]),c_0_166]),c_0_24]),c_0_24]) ).
cnf(c_0_240,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(identity,multiply(b,b))) = greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_234]),c_0_34]),c_0_34]),c_0_44]),c_0_24]),c_0_235]) ).
cnf(c_0_241,plain,
multiply(inverse(greatest_lower_bound(X1,X2)),X1) = least_upper_bound(identity,multiply(inverse(X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_89]),c_0_112]),c_0_112]) ).
cnf(c_0_242,plain,
least_upper_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),least_upper_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_17]),c_0_27]) ).
cnf(c_0_243,hypothesis,
least_upper_bound(a,multiply(greatest_lower_bound(a,b),inverse(b))) = a,
inference(spm,[status(thm)],[c_0_31,c_0_236]) ).
cnf(c_0_244,plain,
multiply(greatest_lower_bound(identity,X1),X1) = multiply(X1,greatest_lower_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_184,c_0_24]) ).
cnf(c_0_245,hypothesis,
greatest_lower_bound(identity,multiply(b,a)) = greatest_lower_bound(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_237]),c_0_34]),c_0_28]),c_0_238]) ).
cnf(c_0_246,hypothesis,
greatest_lower_bound(identity,multiply(greatest_lower_bound(a,b),b)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(b,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_239]),c_0_25]),c_0_25]) ).
cnf(c_0_247,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(greatest_lower_bound(X1,X2),X3))) = multiply(greatest_lower_bound(X1,X2),greatest_lower_bound(X3,identity)),
inference(spm,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_248,hypothesis,
greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),b)) = greatest_lower_bound(a,multiply(b,greatest_lower_bound(b,identity))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_228]),c_0_28]),c_0_240]) ).
cnf(c_0_249,hypothesis,
multiply(inverse(a),multiply(greatest_lower_bound(a,b),multiply(inverse(b),least_upper_bound(a,b)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_175]),c_0_112]),c_0_241]),c_0_242]),c_0_16]),c_0_16]),c_0_242]),c_0_27]),c_0_243]),c_0_17]) ).
cnf(c_0_250,hypothesis,
multiply(greatest_lower_bound(a,b),multiply(b,a)) = multiply(b,multiply(a,greatest_lower_bound(a,b))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_245]),c_0_16]) ).
cnf(c_0_251,hypothesis,
greatest_lower_bound(a,multiply(b,greatest_lower_bound(b,identity))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(b,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_246]),c_0_247]),c_0_34]),c_0_36]),c_0_105]),c_0_34]),c_0_79]),c_0_248]) ).
cnf(c_0_252,plain,
least_upper_bound(multiply(X1,X2),multiply(X2,greatest_lower_bound(identity,X2))) = multiply(least_upper_bound(X1,greatest_lower_bound(identity,X2)),X2),
inference(spm,[status(thm)],[c_0_63,c_0_244]) ).
cnf(c_0_253,hypothesis,
multiply(greatest_lower_bound(a,b),multiply(inverse(b),least_upper_bound(a,b))) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_249]),c_0_25]),c_0_22]) ).
cnf(c_0_254,plain,
multiply(X1,inverse(multiply(X2,multiply(X3,X1)))) = inverse(multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_46,c_0_16]) ).
cnf(c_0_255,hypothesis,
multiply(inverse(greatest_lower_bound(a,b)),multiply(b,multiply(a,greatest_lower_bound(a,b)))) = multiply(b,a),
inference(spm,[status(thm)],[c_0_19,c_0_250]) ).
cnf(c_0_256,hypothesis,
multiply(inverse(b),greatest_lower_bound(a,b)) = greatest_lower_bound(a,inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_245]),c_0_22]),c_0_24]) ).
cnf(c_0_257,hypothesis,
greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),b)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(b,identity)),
inference(rw,[status(thm)],[c_0_248,c_0_251]) ).
cnf(c_0_258,plain,
greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_259,hypothesis,
least_upper_bound(a,multiply(inverse(b),least_upper_bound(a,b))) = multiply(inverse(b),least_upper_bound(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_106]),c_0_22]),c_0_106]),c_0_27]),c_0_153]),c_0_18]) ).
cnf(c_0_260,plain,
inverse(multiply(X1,multiply(X2,inverse(X3)))) = multiply(X3,inverse(multiply(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_54]),c_0_16]),c_0_83]) ).
cnf(c_0_261,hypothesis,
multiply(a,multiply(greatest_lower_bound(a,b),inverse(multiply(b,a)))) = greatest_lower_bound(a,inverse(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_255]),c_0_16]),c_0_112]),c_0_256]) ).
cnf(c_0_262,hypothesis,
greatest_lower_bound(b,multiply(inverse(b),least_upper_bound(a,b))) = greatest_lower_bound(b,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_257]),c_0_19]),c_0_241]),c_0_242]),c_0_24]) ).
cnf(c_0_263,hypothesis,
greatest_lower_bound(a,least_upper_bound(X1,multiply(inverse(b),least_upper_bound(a,b)))) = a,
inference(spm,[status(thm)],[c_0_258,c_0_259]) ).
cnf(c_0_264,hypothesis,
multiply(b,multiply(a,inverse(multiply(a,greatest_lower_bound(a,b))))) = least_upper_bound(b,inverse(a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_204]),c_0_27]),c_0_16]) ).
cnf(c_0_265,hypothesis,
greatest_lower_bound(multiply(b,b),least_upper_bound(a,b)) = multiply(b,greatest_lower_bound(b,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_262]),c_0_25]),c_0_25]) ).
cnf(c_0_266,plain,
least_upper_bound(X1,multiply(X2,multiply(X3,X1))) = multiply(least_upper_bound(X2,inverse(X3)),multiply(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_19]),c_0_27]) ).
cnf(c_0_267,hypothesis,
greatest_lower_bound(a,multiply(inverse(b),least_upper_bound(X1,least_upper_bound(a,b)))) = a,
inference(spm,[status(thm)],[c_0_263,c_0_68]) ).
cnf(c_0_268,hypothesis,
greatest_lower_bound(b,greatest_lower_bound(identity,inverse(a))) = greatest_lower_bound(b,inverse(a)),
inference(spm,[status(thm)],[c_0_72,c_0_49]) ).
cnf(c_0_269,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_270,plain,
greatest_lower_bound(X1,multiply(X2,multiply(X3,X1))) = multiply(greatest_lower_bound(identity,multiply(X2,X3)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_16]),c_0_24]) ).
cnf(c_0_271,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_125]),c_0_112]) ).
cnf(c_0_272,plain,
multiply(greatest_lower_bound(X1,multiply(X2,X3)),inverse(greatest_lower_bound(multiply(inverse(X2),X1),X3))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_57]),c_0_25]) ).
cnf(c_0_273,plain,
multiply(X1,inverse(multiply(X2,multiply(X1,greatest_lower_bound(identity,multiply(X2,X1)))))) = inverse(multiply(greatest_lower_bound(identity,multiply(X2,X1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_244]),c_0_16]) ).
cnf(c_0_274,hypothesis,
multiply(a,multiply(greatest_lower_bound(a,b),inverse(a))) = greatest_lower_bound(identity,multiply(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_264]),c_0_169]),c_0_24]),c_0_128]),c_0_54]),c_0_16]) ).
cnf(c_0_275,hypothesis,
multiply(greatest_lower_bound(b,identity),greatest_lower_bound(a,identity)) = greatest_lower_bound(a,b),
inference(rw,[status(thm)],[c_0_198,c_0_245]) ).
cnf(c_0_276,hypothesis,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(b,identity)) = greatest_lower_bound(a,multiply(b,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_265]),c_0_251]) ).
cnf(c_0_277,plain,
multiply(inverse(greatest_lower_bound(identity,X1)),multiply(X1,greatest_lower_bound(identity,X1))) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_244]) ).
cnf(c_0_278,plain,
multiply(least_upper_bound(X1,inverse(X2)),multiply(X2,X3)) = multiply(least_upper_bound(identity,multiply(X1,X2)),X3),
inference(rw,[status(thm)],[c_0_266,c_0_134]) ).
cnf(c_0_279,plain,
greatest_lower_bound(least_upper_bound(X1,X2),greatest_lower_bound(X3,least_upper_bound(X2,X1))) = greatest_lower_bound(X3,least_upper_bound(X2,X1)),
inference(spm,[status(thm)],[c_0_50,c_0_139]) ).
cnf(c_0_280,hypothesis,
greatest_lower_bound(multiply(b,a),least_upper_bound(X1,least_upper_bound(a,b))) = multiply(b,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_267]),c_0_25]),c_0_25]) ).
cnf(c_0_281,hypothesis,
greatest_lower_bound(b,inverse(least_upper_bound(a,identity))) = greatest_lower_bound(b,inverse(a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_268,c_0_147]),c_0_27]) ).
cnf(c_0_282,plain,
least_upper_bound(X1,least_upper_bound(multiply(X2,X1),X3)) = least_upper_bound(X3,multiply(least_upper_bound(X2,identity),X1)),
inference(spm,[status(thm)],[c_0_269,c_0_75]) ).
cnf(c_0_283,hypothesis,
greatest_lower_bound(multiply(b,a),multiply(a,greatest_lower_bound(a,b))) = multiply(a,greatest_lower_bound(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_270,c_0_255]),c_0_271]),c_0_18]),c_0_24]) ).
cnf(c_0_284,hypothesis,
multiply(greatest_lower_bound(a,b),least_upper_bound(b,inverse(a))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_245]),c_0_22]),c_0_24]),c_0_204]),c_0_27]) ).
cnf(c_0_285,plain,
multiply(inverse(greatest_lower_bound(X1,X2)),X2) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_125]),c_0_112]),c_0_112]) ).
cnf(c_0_286,hypothesis,
multiply(a,inverse(multiply(b,multiply(a,greatest_lower_bound(a,b))))) = inverse(multiply(greatest_lower_bound(a,b),b)),
inference(spm,[status(thm)],[c_0_273,c_0_245]) ).
cnf(c_0_287,hypothesis,
multiply(greatest_lower_bound(a,b),inverse(a)) = greatest_lower_bound(b,inverse(a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_274]),c_0_57]),c_0_22]),c_0_24]) ).
cnf(c_0_288,hypothesis,
multiply(greatest_lower_bound(b,identity),greatest_lower_bound(a,b)) = greatest_lower_bound(a,multiply(b,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_275]),c_0_34]),c_0_28]),c_0_34]),c_0_36]),c_0_251]),c_0_276]),c_0_34]),c_0_24]),c_0_79]) ).
cnf(c_0_289,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_277,c_0_195]),c_0_278]),c_0_18]) ).
cnf(c_0_290,hypothesis,
greatest_lower_bound(identity,multiply(greatest_lower_bound(a,b),b)) = greatest_lower_bound(a,multiply(b,b)),
inference(rw,[status(thm)],[c_0_246,c_0_276]) ).
cnf(c_0_291,hypothesis,
least_upper_bound(identity,multiply(greatest_lower_bound(a,b),b)) = least_upper_bound(b,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_233]),c_0_25]),c_0_25]),c_0_99]),c_0_18]),c_0_27]) ).
cnf(c_0_292,hypothesis,
greatest_lower_bound(multiply(b,a),least_upper_bound(a,least_upper_bound(b,X1))) = multiply(b,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_280]),c_0_33]),c_0_24]) ).
cnf(c_0_293,hypothesis,
least_upper_bound(b,least_upper_bound(identity,multiply(a,b))) = least_upper_bound(identity,multiply(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_281]),c_0_204]),c_0_27]),c_0_99]),c_0_25]),c_0_282]),c_0_27]) ).
cnf(c_0_294,plain,
least_upper_bound(X1,least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(X2,multiply(X1,least_upper_bound(X3,identity))),
inference(spm,[status(thm)],[c_0_71,c_0_74]) ).
cnf(c_0_295,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(b,multiply(inverse(a),multiply(b,a)))) = greatest_lower_bound(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_283]),c_0_19]),c_0_24]),c_0_34]) ).
cnf(c_0_296,hypothesis,
multiply(inverse(a),greatest_lower_bound(a,b)) = multiply(inverse(least_upper_bound(a,b)),b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_253]),c_0_112]) ).
cnf(c_0_297,plain,
multiply(inverse(greatest_lower_bound(X1,identity)),multiply(X1,greatest_lower_bound(X1,identity))) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_184]) ).
cnf(c_0_298,hypothesis,
multiply(inverse(a),least_upper_bound(a,b)) = least_upper_bound(b,inverse(a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_284]),c_0_285]),c_0_242]),c_0_27]) ).
cnf(c_0_299,hypothesis,
multiply(b,greatest_lower_bound(identity,multiply(a,b))) = multiply(greatest_lower_bound(a,b),b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_286]),c_0_25]),c_0_16]),c_0_16]),c_0_287]),c_0_111]) ).
cnf(c_0_300,hypothesis,
greatest_lower_bound(identity,multiply(b,greatest_lower_bound(a,b))) = greatest_lower_bound(a,multiply(b,b)),
inference(rw,[status(thm)],[c_0_213,c_0_288]) ).
cnf(c_0_301,hypothesis,
multiply(least_upper_bound(b,identity),greatest_lower_bound(a,multiply(b,b))) = multiply(greatest_lower_bound(a,b),b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_290]),c_0_291]) ).
cnf(c_0_302,hypothesis,
greatest_lower_bound(multiply(b,a),least_upper_bound(a,least_upper_bound(identity,multiply(a,b)))) = multiply(b,a),
inference(spm,[status(thm)],[c_0_292,c_0_293]) ).
cnf(c_0_303,hypothesis,
least_upper_bound(a,least_upper_bound(identity,multiply(a,b))) = least_upper_bound(identity,multiply(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_174]),c_0_204]),c_0_27]),c_0_214]),c_0_25]),c_0_294]) ).
cnf(c_0_304,hypothesis,
greatest_lower_bound(b,multiply(inverse(least_upper_bound(a,b)),multiply(b,a))) = greatest_lower_bound(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_295]),c_0_34]),c_0_24]),c_0_34]),c_0_295]),c_0_67]),c_0_24]),c_0_34]),c_0_24]),c_0_270]),c_0_125]),c_0_24]),c_0_296]),c_0_16]) ).
cnf(c_0_305,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_297,c_0_183]),c_0_278]),c_0_18]) ).
cnf(c_0_306,hypothesis,
least_upper_bound(identity,multiply(a,b)) = least_upper_bound(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_298]),c_0_25]),c_0_214]) ).
cnf(c_0_307,hypothesis,
multiply(inverse(b),multiply(greatest_lower_bound(a,b),b)) = greatest_lower_bound(identity,multiply(a,b)),
inference(spm,[status(thm)],[c_0_19,c_0_299]) ).
cnf(c_0_308,hypothesis,
multiply(greatest_lower_bound(a,b),b) = multiply(b,greatest_lower_bound(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_300]),c_0_226]),c_0_301]) ).
cnf(c_0_309,hypothesis,
greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(a,b))) = multiply(b,a),
inference(rw,[status(thm)],[c_0_302,c_0_303]) ).
cnf(c_0_310,hypothesis,
greatest_lower_bound(multiply(b,a),multiply(least_upper_bound(a,b),b)) = multiply(least_upper_bound(a,b),greatest_lower_bound(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_304]),c_0_25]),c_0_25]),c_0_24]) ).
cnf(c_0_311,hypothesis,
multiply(least_upper_bound(a,b),greatest_lower_bound(identity,multiply(a,b))) = multiply(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_306]),c_0_24]) ).
cnf(c_0_312,hypothesis,
greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_307,c_0_308]),c_0_19]) ).
cnf(c_0_313,plain,
multiply(greatest_lower_bound(X1,identity),least_upper_bound(identity,X1)) = multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_200]),c_0_105]) ).
cnf(c_0_314,plain,
multiply(greatest_lower_bound(identity,X1),least_upper_bound(X1,identity)) = multiply(least_upper_bound(X1,identity),greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_244]),c_0_75]) ).
cnf(c_0_315,plain,
multiply(least_upper_bound(X1,identity),greatest_lower_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_74]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_316,hypothesis,
least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(b,a))) = least_upper_bound(identity,multiply(a,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_309]),c_0_33]) ).
cnf(c_0_317,hypothesis,
least_upper_bound(multiply(b,a),multiply(least_upper_bound(a,b),greatest_lower_bound(a,b))) = multiply(b,a),
inference(spm,[status(thm)],[c_0_31,c_0_310]) ).
cnf(c_0_318,hypothesis,
multiply(least_upper_bound(a,b),greatest_lower_bound(a,b)) = multiply(a,b),
inference(rw,[status(thm)],[c_0_311,c_0_312]) ).
cnf(c_0_319,plain,
multiply(greatest_lower_bound(X1,identity),least_upper_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[c_0_313,c_0_305]) ).
cnf(c_0_320,plain,
multiply(greatest_lower_bound(identity,X1),least_upper_bound(X1,identity)) = X1,
inference(rw,[status(thm)],[c_0_314,c_0_315]) ).
cnf(c_0_321,hypothesis,
least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(b,a))) = least_upper_bound(a,b),
inference(rw,[status(thm)],[c_0_316,c_0_306]) ).
cnf(c_0_322,hypothesis,
least_upper_bound(multiply(a,b),multiply(b,a)) = multiply(b,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_317,c_0_318]),c_0_27]) ).
cnf(c_0_323,hypothesis,
multiply(greatest_lower_bound(identity,multiply(a,b)),least_upper_bound(a,b)) = multiply(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_319,c_0_306]),c_0_24]) ).
cnf(c_0_324,negated_conjecture,
multiply(a,b) != multiply(b,a),
inference(fof_simplification,[status(thm)],[prove_p33]) ).
cnf(c_0_325,hypothesis,
multiply(greatest_lower_bound(a,b),least_upper_bound(identity,multiply(b,a))) = multiply(b,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_320,c_0_245]),c_0_27]) ).
cnf(c_0_326,hypothesis,
least_upper_bound(identity,multiply(b,a)) = least_upper_bound(a,b),
inference(rw,[status(thm)],[c_0_321,c_0_322]) ).
cnf(c_0_327,hypothesis,
multiply(greatest_lower_bound(a,b),least_upper_bound(a,b)) = multiply(a,b),
inference(rw,[status(thm)],[c_0_323,c_0_312]) ).
cnf(c_0_328,negated_conjecture,
multiply(a,b) != multiply(b,a),
c_0_324 ).
cnf(c_0_329,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_325,c_0_326]),c_0_327]),c_0_328]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP187-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:04:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 89.78/13.56 % Version: 3.5.1
% 89.78/13.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 89.78/13.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 89.78/13.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 89.78/13.56 % Starting new_bool_3 with 300s (1) cores
% 89.78/13.56 % Starting new_bool_1 with 300s (1) cores
% 89.78/13.56 % Starting sh5l with 300s (1) cores
% 89.78/13.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3295922 completed with status 0
% 89.78/13.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 89.78/13.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 89.78/13.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 89.78/13.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 89.78/13.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 89.78/13.56 % No SInE strategy applied
% 89.78/13.56 % Search class: FUUPM-FFSF21-MFFFFFNN
% 89.78/13.56 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 89.78/13.56 % Starting SubtermCWHack with 136s (1) cores
% 89.78/13.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 89.78/13.56 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 89.78/13.56 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 89.78/13.56 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 89.78/13.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3295928 completed with status 0
% 89.78/13.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 89.78/13.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 89.78/13.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 89.78/13.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 89.78/13.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 89.78/13.56 % No SInE strategy applied
% 89.78/13.56 % Search class: FUUPM-FFSF21-MFFFFFNN
% 89.78/13.56 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 89.78/13.56 % Starting SubtermCWHack with 136s (1) cores
% 89.78/13.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 89.78/13.56 % Preprocessing time : 0.001 s
% 89.78/13.56 % Presaturation interreduction done
% 89.78/13.56
% 89.78/13.56 % Proof found!
% 89.78/13.56 % SZS status Unsatisfiable
% 89.78/13.56 % SZS output start CNFRefutation
% See solution above
% 89.78/13.56 % Parsed axioms : 17
% 89.78/13.56 % Removed by relevancy pruning/SinE : 0
% 89.78/13.56 % Initial clauses : 17
% 89.78/13.56 % Removed in clause preprocessing : 0
% 89.78/13.56 % Initial clauses in saturation : 17
% 89.78/13.56 % Processed clauses : 15737
% 89.78/13.56 % ...of these trivial : 6234
% 89.78/13.56 % ...subsumed : 7097
% 89.78/13.56 % ...remaining for further processing : 2406
% 89.78/13.56 % Other redundant clauses eliminated : 0
% 89.78/13.56 % Clauses deleted for lack of memory : 0
% 89.78/13.56 % Backward-subsumed : 1
% 89.78/13.56 % Backward-rewritten : 408
% 89.78/13.56 % Generated clauses : 777570
% 89.78/13.56 % ...of the previous two non-redundant : 517289
% 89.78/13.56 % ...aggressively subsumed : 0
% 89.78/13.56 % Contextual simplify-reflections : 0
% 89.78/13.56 % Paramodulations : 777570
% 89.78/13.56 % Factorizations : 0
% 89.78/13.56 % NegExts : 0
% 89.78/13.56 % Equation resolutions : 0
% 89.78/13.56 % Disequality decompositions : 0
% 89.78/13.56 % Total rewrite steps : 1192344
% 89.78/13.56 % ...of those cached : 969876
% 89.78/13.56 % Propositional unsat checks : 0
% 89.78/13.56 % Propositional check models : 0
% 89.78/13.56 % Propositional check unsatisfiable : 0
% 89.78/13.56 % Propositional clauses : 0
% 89.78/13.56 % Propositional clauses after purity: 0
% 89.78/13.56 % Propositional unsat core size : 0
% 89.78/13.56 % Propositional preprocessing time : 0.000
% 89.78/13.56 % Propositional encoding time : 0.000
% 89.78/13.56 % Propositional solver time : 0.000
% 89.78/13.56 % Success case prop preproc time : 0.000
% 89.78/13.56 % Success case prop encoding time : 0.000
% 89.78/13.56 % Success case prop solver time : 0.000
% 89.78/13.56 % Current number of processed clauses : 1980
% 89.78/13.56 % Positive orientable unit clauses : 1907
% 89.78/13.56 % Positive unorientable unit clauses: 72
% 89.78/13.56 % Negative unit clauses : 1
% 89.78/13.56 % Non-unit-clauses : 0
% 89.78/13.56 % Current number of unprocessed clauses: 500806
% 89.78/13.56 % ...number of literals in the above : 500806
% 89.78/13.56 % Current number of archived formulas : 0
% 89.78/13.56 % Current number of archived clauses : 426
% 89.78/13.56 % Clause-clause subsumption calls (NU) : 0
% 89.78/13.56 % Rec. Clause-clause subsumption calls : 0
% 89.78/13.56 % Non-unit clause-clause subsumptions : 0
% 89.78/13.56 % Unit Clause-clause subsumption calls : 544
% 89.78/13.56 % Rewrite failures with RHS unbound : 0
% 89.78/13.56 % BW rewrite match attempts : 19045
% 89.78/13.56 % BW rewrite match successes : 1049
% 89.78/13.56 % Condensation attempts : 0
% 89.78/13.56 % Condensation successes : 0
% 89.78/13.56 % Termbank termtop insertions : 13546541
% 89.78/13.56 % Search garbage collected termcells : 2
% 89.78/13.56
% 89.78/13.56 % -------------------------------------------------
% 89.78/13.56 % User time : 11.791 s
% 89.78/13.56 % System time : 0.512 s
% 89.78/13.56 % Total time : 12.303 s
% 89.78/13.56 % Maximum resident set size: 3640 pages
% 89.78/13.56
% 89.78/13.56 % -------------------------------------------------
% 89.78/13.56 % User time : 61.108 s
% 89.78/13.56 % System time : 2.493 s
% 89.78/13.56 % Total time : 63.601 s
% 89.78/13.56 % Maximum resident set size: 4864 pages
% 89.78/13.56 % E exiting
%------------------------------------------------------------------------------