TSTP Solution File: GRP164-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP164-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n008.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 : Thu Aug 31 00:17:21 EDT 2023
% Result : Unsatisfiable 119.22s 119.22s
% Output : CNFRefutation 119.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 23
% Syntax : Number of formulae : 223 ( 215 unt; 8 typ; 0 def)
% Number of atoms : 215 ( 214 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 459 ( 52 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(decl_26,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
c: $i ).
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_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(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(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(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(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(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(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(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(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(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(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(prove_distrnu,negated_conjecture,
least_upper_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distrnu) ).
cnf(c_0_15,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_16,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_17,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_18,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_19,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_20,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_21,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_23,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_24,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_25,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_26,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_27,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_24]),c_0_21]) ).
cnf(c_0_28,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_29,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_25,c_0_17]),c_0_26]) ).
cnf(c_0_30,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_31,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_32,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_27]),c_0_22]) ).
cnf(c_0_33,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_34,plain,
multiply(greatest_lower_bound(X1,identity),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_23]),c_0_26]) ).
cnf(c_0_35,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_25,c_0_16]),c_0_26]) ).
cnf(c_0_36,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_37,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_30,c_0_21]),c_0_31]) ).
cnf(c_0_38,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_39,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_40,plain,
multiply(greatest_lower_bound(X1,inverse(multiply(X2,X3))),X2) = greatest_lower_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_41,plain,
multiply(X1,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
multiply(greatest_lower_bound(X1,greatest_lower_bound(X2,inverse(X3))),X3) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,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_37,c_0_16]),c_0_31]) ).
cnf(c_0_44,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_38,c_0_22]) ).
cnf(c_0_45,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_30,c_0_23]),c_0_31]) ).
cnf(c_0_46,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_47,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_39,c_0_21]),c_0_26]) ).
cnf(c_0_48,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_49,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_50,plain,
greatest_lower_bound(X1,greatest_lower_bound(identity,multiply(X2,X1))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X2,identity),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_41]),c_0_22]),c_0_42]),c_0_22]),c_0_26]),c_0_36]) ).
cnf(c_0_51,plain,
multiply(inverse(X1),least_upper_bound(identity,X1)) = least_upper_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_43,c_0_31]) ).
cnf(c_0_52,plain,
multiply(X1,least_upper_bound(X2,inverse(multiply(X3,X1)))) = least_upper_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_53,plain,
multiply(inverse(least_upper_bound(X1,identity)),X1) = inverse(least_upper_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_54,plain,
multiply(X1,least_upper_bound(X2,least_upper_bound(X3,inverse(X1)))) = least_upper_bound(identity,multiply(X1,least_upper_bound(X2,X3))),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,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_47,c_0_16]),c_0_26]) ).
cnf(c_0_56,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_31]) ).
cnf(c_0_57,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_26]) ).
cnf(c_0_58,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(identity,X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_48]),c_0_26]),c_0_48]),c_0_26]) ).
cnf(c_0_59,plain,
least_upper_bound(X1,least_upper_bound(identity,multiply(X1,X2))) = least_upper_bound(identity,multiply(X1,least_upper_bound(X2,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_52,c_0_53]),c_0_22]),c_0_54]),c_0_22]),c_0_31]),c_0_46]) ).
cnf(c_0_60,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_61,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_62,plain,
multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_55,c_0_26]) ).
cnf(c_0_63,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_26]) ).
cnf(c_0_64,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,inverse(X1)))) = identity,
inference(spm,[status(thm)],[c_0_58,c_0_22]) ).
cnf(c_0_65,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,inverse(X1)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_49]),c_0_31]),c_0_49]),c_0_31]) ).
cnf(c_0_66,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_61,c_0_17]),c_0_31]) ).
cnf(c_0_67,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_56]),c_0_31]) ).
cnf(c_0_68,plain,
multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X3))) = greatest_lower_bound(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_39,c_0_28]) ).
cnf(c_0_69,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_16]) ).
cnf(c_0_70,plain,
multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,inverse(X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_64]),c_0_31]),c_0_65]) ).
cnf(c_0_71,plain,
multiply(least_upper_bound(X1,identity),X1) = multiply(X1,least_upper_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_37,c_0_66]) ).
cnf(c_0_72,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_46,c_0_57]) ).
cnf(c_0_73,plain,
least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_67]),c_0_46]),c_0_46]) ).
cnf(c_0_74,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_36,c_0_48]) ).
cnf(c_0_75,plain,
multiply(inverse(greatest_lower_bound(multiply(X1,X2),X3)),X1) = inverse(greatest_lower_bound(X2,multiply(inverse(X1),X3))),
inference(spm,[status(thm)],[c_0_32,c_0_68]) ).
cnf(c_0_76,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_41]),c_0_26]),c_0_69]),c_0_21]) ).
cnf(c_0_77,plain,
multiply(greatest_lower_bound(inverse(multiply(X1,X2)),X3),X1) = greatest_lower_bound(inverse(X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_78,plain,
least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_70]),c_0_21]) ).
cnf(c_0_79,plain,
multiply(X1,inverse(greatest_lower_bound(identity,X1))) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_33,c_0_60]) ).
cnf(c_0_80,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_57,c_0_36]) ).
cnf(c_0_81,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_46,c_0_49]) ).
cnf(c_0_82,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_71,c_0_31]) ).
cnf(c_0_83,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_48]),c_0_46]),c_0_46]),c_0_73]) ).
cnf(c_0_84,plain,
least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,least_upper_bound(X1,X2)))) = least_upper_bound(X1,X2),
inference(spm,[status(thm)],[c_0_57,c_0_46]) ).
cnf(c_0_85,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(least_upper_bound(X1,X3),X2)) = greatest_lower_bound(least_upper_bound(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_74]),c_0_31]) ).
cnf(c_0_86,plain,
inverse(greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(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_75,c_0_76]),c_0_32]),c_0_38]),c_0_40]),c_0_17]) ).
cnf(c_0_87,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_36,c_0_47]) ).
cnf(c_0_88,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld ).
cnf(c_0_89,plain,
multiply(greatest_lower_bound(X1,identity),X1) = multiply(X1,greatest_lower_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_47,c_0_29]) ).
cnf(c_0_90,plain,
multiply(greatest_lower_bound(multiply(X1,inverse(X2)),X3),X2) = greatest_lower_bound(X1,multiply(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_33]),c_0_22]) ).
cnf(c_0_91,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_30,c_0_18]) ).
cnf(c_0_92,plain,
inverse(greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_78]),c_0_79]),c_0_21]) ).
cnf(c_0_93,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_36,c_0_56]) ).
cnf(c_0_94,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = greatest_lower_bound(X2,greatest_lower_bound(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_63]),c_0_36]),c_0_36]) ).
cnf(c_0_95,plain,
least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,X1))) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_48]),c_0_46]) ).
cnf(c_0_96,plain,
least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) = least_upper_bound(X2,least_upper_bound(X3,X1)),
inference(spm,[status(thm)],[c_0_67,c_0_46]) ).
cnf(c_0_97,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_49,c_0_36]) ).
cnf(c_0_98,plain,
least_upper_bound(X1,least_upper_bound(multiply(greatest_lower_bound(X2,identity),X1),X3)) = least_upper_bound(X1,X3),
inference(spm,[status(thm)],[c_0_81,c_0_29]) ).
cnf(c_0_99,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(X1,identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_34]),c_0_22]) ).
cnf(c_0_100,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) = multiply(greatest_lower_bound(X1,identity),least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_82]),c_0_29]) ).
cnf(c_0_101,plain,
least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X3,least_upper_bound(X2,X1)))) = least_upper_bound(X2,X1),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_102,plain,
least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,X3))) = greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,X3)),
inference(spm,[status(thm)],[c_0_85,c_0_48]) ).
cnf(c_0_103,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_86]),c_0_22]) ).
cnf(c_0_104,plain,
multiply(greatest_lower_bound(X1,multiply(X2,X3)),inverse(X3)) = greatest_lower_bound(multiply(X1,inverse(X3)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_22]),c_0_22]) ).
cnf(c_0_105,plain,
greatest_lower_bound(identity,multiply(X1,greatest_lower_bound(X1,identity))) = multiply(greatest_lower_bound(X1,identity),greatest_lower_bound(X1,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_87]),c_0_36]),c_0_88]),c_0_89]) ).
cnf(c_0_106,plain,
multiply(X1,inverse(greatest_lower_bound(X2,multiply(X3,X1)))) = inverse(greatest_lower_bound(multiply(X2,inverse(X1)),X3)),
inference(spm,[status(thm)],[c_0_27,c_0_90]) ).
cnf(c_0_107,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_108,plain,
multiply(inverse(least_upper_bound(X1,multiply(X2,X3))),X2) = inverse(least_upper_bound(multiply(inverse(X2),X1),X3)),
inference(spm,[status(thm)],[c_0_44,c_0_91]) ).
cnf(c_0_109,plain,
inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_92]) ).
cnf(c_0_110,plain,
multiply(X1,greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_39,c_0_23]) ).
cnf(c_0_111,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_49]),c_0_36]),c_0_36]),c_0_94]) ).
cnf(c_0_112,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X3,greatest_lower_bound(X1,X2)))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_56,c_0_36]) ).
cnf(c_0_113,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(greatest_lower_bound(X1,X3),X2)) = least_upper_bound(greatest_lower_bound(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_81]),c_0_26]) ).
cnf(c_0_114,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_48]),c_0_46]),c_0_46]),c_0_96]) ).
cnf(c_0_115,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_97,c_0_63]) ).
cnf(c_0_116,plain,
least_upper_bound(X1,least_upper_bound(multiply(greatest_lower_bound(identity,X2),X1),X3)) = least_upper_bound(X1,X3),
inference(spm,[status(thm)],[c_0_98,c_0_26]) ).
cnf(c_0_117,plain,
multiply(greatest_lower_bound(X1,identity),least_upper_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_92]),c_0_100]) ).
cnf(c_0_118,plain,
least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X2,X3),least_upper_bound(X2,X1))) = least_upper_bound(X2,X1),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_119,plain,
greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_103,c_0_22]) ).
cnf(c_0_120,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X1,identity))) = greatest_lower_bound(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_104,c_0_105]),c_0_15]),c_0_23]),c_0_21]),c_0_17]),c_0_26]) ).
cnf(c_0_121,plain,
inverse(greatest_lower_bound(inverse(X1),X2)) = least_upper_bound(X1,inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_78]),c_0_106]),c_0_17]),c_0_21]) ).
cnf(c_0_122,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_107]) ).
cnf(c_0_123,plain,
inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(X1,inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_40]),c_0_17]),c_0_21]) ).
cnf(c_0_124,plain,
greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X2,X1)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_103]),c_0_23]),c_0_22]) ).
cnf(c_0_125,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X3,greatest_lower_bound(X2,X1)))) = greatest_lower_bound(X2,X1),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_126,plain,
greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,X3))) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,X3)),
inference(spm,[status(thm)],[c_0_113,c_0_49]) ).
cnf(c_0_127,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X2,X1)),
inference(spm,[status(thm)],[c_0_83,c_0_114]) ).
cnf(c_0_128,plain,
least_upper_bound(greatest_lower_bound(X1,X2),least_upper_bound(greatest_lower_bound(X2,X1),X3)) = least_upper_bound(greatest_lower_bound(X1,X2),X3),
inference(spm,[status(thm)],[c_0_46,c_0_115]) ).
cnf(c_0_129,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_39,c_0_18]) ).
cnf(c_0_130,plain,
least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),least_upper_bound(X1,X3))) = least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),X3)),
inference(spm,[status(thm)],[c_0_116,c_0_30]) ).
cnf(c_0_131,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(X1,X2)),least_upper_bound(X1,identity)) = greatest_lower_bound(least_upper_bound(X1,X2),least_upper_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_117,c_0_118]),c_0_36]),c_0_26]),c_0_56]),c_0_26]) ).
cnf(c_0_132,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_119,c_0_56]),c_0_26]) ).
cnf(c_0_133,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_80,c_0_26]) ).
cnf(c_0_134,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(identity,least_upper_bound(X2,X1)))) = greatest_lower_bound(X1,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_120]),c_0_93]),c_0_26]) ).
cnf(c_0_135,plain,
inverse(greatest_lower_bound(X1,inverse(X2))) = least_upper_bound(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_121,c_0_26]) ).
cnf(c_0_136,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_16,c_0_122]) ).
cnf(c_0_137,plain,
greatest_lower_bound(inverse(X1),inverse(X2)) = inverse(least_upper_bound(X1,X2)),
inference(spm,[status(thm)],[c_0_123,c_0_22]) ).
cnf(c_0_138,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(X1,X2),inverse(X1))) = identity,
inference(spm,[status(thm)],[c_0_124,c_0_48]) ).
cnf(c_0_139,plain,
greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X2,X3),greatest_lower_bound(X2,X1))) = greatest_lower_bound(X2,X1),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_140,plain,
least_upper_bound(greatest_lower_bound(X1,X2),X3) = least_upper_bound(X3,greatest_lower_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_115]),c_0_128]) ).
cnf(c_0_141,plain,
multiply(X1,greatest_lower_bound(X2,least_upper_bound(multiply(inverse(X1),X3),X4))) = greatest_lower_bound(multiply(X1,X2),least_upper_bound(X3,multiply(X1,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_91]),c_0_22]),c_0_22]) ).
cnf(c_0_142,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,identity)) = least_upper_bound(X1,greatest_lower_bound(identity,least_upper_bound(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_102]),c_0_21]) ).
cnf(c_0_143,plain,
multiply(X1,least_upper_bound(multiply(inverse(X1),X2),X3)) = least_upper_bound(X2,multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_144,plain,
greatest_lower_bound(identity,multiply(inverse(X1),least_upper_bound(X2,X1))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_132]),c_0_16]) ).
cnf(c_0_145,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(identity,X1))) = greatest_lower_bound(identity,X1),
inference(spm,[status(thm)],[c_0_120,c_0_26]) ).
cnf(c_0_146,plain,
multiply(X1,multiply(least_upper_bound(X2,inverse(X1)),X3)) = multiply(least_upper_bound(identity,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_15,c_0_45]) ).
cnf(c_0_147,plain,
multiply(least_upper_bound(identity,inverse(X1)),inverse(least_upper_bound(X1,identity))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_53]),c_0_22]) ).
cnf(c_0_148,plain,
least_upper_bound(X1,greatest_lower_bound(X2,multiply(greatest_lower_bound(X3,identity),X1))) = X1,
inference(spm,[status(thm)],[c_0_133,c_0_29]) ).
cnf(c_0_149,plain,
multiply(X1,least_upper_bound(inverse(X1),X2)) = least_upper_bound(identity,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_150,plain,
least_upper_bound(X1,greatest_lower_bound(identity,least_upper_bound(X2,inverse(X1)))) = least_upper_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_121,c_0_134]),c_0_26]),c_0_135]),c_0_136]),c_0_22]) ).
cnf(c_0_151,plain,
inverse(greatest_lower_bound(identity,multiply(X1,inverse(X2)))) = least_upper_bound(identity,multiply(X2,inverse(X1))),
inference(spm,[status(thm)],[c_0_78,c_0_33]) ).
cnf(c_0_152,plain,
multiply(X1,inverse(least_upper_bound(X1,X2))) = greatest_lower_bound(identity,multiply(X1,inverse(X2))),
inference(spm,[status(thm)],[c_0_110,c_0_137]) ).
cnf(c_0_153,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_26]) ).
cnf(c_0_154,plain,
least_upper_bound(identity,multiply(least_upper_bound(X1,X2),inverse(X1))) = multiply(least_upper_bound(X1,X2),inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_138]),c_0_31]) ).
cnf(c_0_155,plain,
greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X2,X3))) = greatest_lower_bound(X2,X1),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_156,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,multiply(X2,X3))) = least_upper_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,multiply(X2,X3)))),
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_141,c_0_142]),c_0_143]),c_0_141]),c_0_21]),c_0_143]),c_0_21]),c_0_26]) ).
cnf(c_0_157,plain,
inverse(greatest_lower_bound(identity,multiply(inverse(X1),X2))) = least_upper_bound(identity,multiply(inverse(X2),X1)),
inference(spm,[status(thm)],[c_0_78,c_0_44]) ).
cnf(c_0_158,plain,
multiply(inverse(least_upper_bound(X1,X2)),X2) = greatest_lower_bound(identity,multiply(inverse(X1),X2)),
inference(spm,[status(thm)],[c_0_35,c_0_137]) ).
cnf(c_0_159,plain,
least_upper_bound(identity,multiply(inverse(X1),least_upper_bound(X2,X1))) = multiply(inverse(X1),least_upper_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_144]),c_0_31]) ).
cnf(c_0_160,plain,
least_upper_bound(X1,greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_145]),c_0_92]),c_0_22]) ).
cnf(c_0_161,plain,
least_upper_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,X3))) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_74]),c_0_46]) ).
cnf(c_0_162,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_47,c_0_38]),c_0_26]) ).
cnf(c_0_163,plain,
multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_23]),c_0_21]) ).
cnf(c_0_164,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_62,c_0_48]),c_0_21]) ).
cnf(c_0_165,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_66,c_0_23]),c_0_31]) ).
cnf(c_0_166,plain,
least_upper_bound(X1,greatest_lower_bound(X2,multiply(greatest_lower_bound(identity,X3),X1))) = X1,
inference(spm,[status(thm)],[c_0_148,c_0_26]) ).
cnf(c_0_167,plain,
least_upper_bound(identity,multiply(X1,greatest_lower_bound(identity,least_upper_bound(X2,X1)))) = least_upper_bound(X1,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(spm,[status(thm)],[c_0_149,c_0_150]),c_0_31]),c_0_78]),c_0_79]),c_0_135]),c_0_136]),c_0_22]) ).
cnf(c_0_168,plain,
least_upper_bound(multiply(X1,X2),greatest_lower_bound(X3,multiply(X1,greatest_lower_bound(X2,X4)))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_133,c_0_39]) ).
cnf(c_0_169,plain,
multiply(least_upper_bound(X1,X2),inverse(X1)) = least_upper_bound(identity,multiply(X2,inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]),c_0_151]),c_0_154]) ).
cnf(c_0_170,plain,
greatest_lower_bound(X1,least_upper_bound(X2,greatest_lower_bound(X1,least_upper_bound(X2,X3)))) = greatest_lower_bound(least_upper_bound(X2,X3),X1),
inference(spm,[status(thm)],[c_0_155,c_0_118]) ).
cnf(c_0_171,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(X1,X3)) = least_upper_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,X3))),
inference(spm,[status(thm)],[c_0_156,c_0_28]) ).
cnf(c_0_172,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_48]),c_0_31]) ).
cnf(c_0_173,plain,
multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_153]),c_0_157]),c_0_159]) ).
cnf(c_0_174,plain,
least_upper_bound(X1,greatest_lower_bound(identity,inverse(greatest_lower_bound(X1,X2)))) = least_upper_bound(X1,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_160]),c_0_161]) ).
cnf(c_0_175,plain,
multiply(least_upper_bound(X1,identity),inverse(least_upper_bound(identity,X1))) = 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(spm,[status(thm)],[c_0_162,c_0_163]),c_0_22]),c_0_136]),c_0_26]),c_0_56]),c_0_22]),c_0_164]) ).
cnf(c_0_176,plain,
multiply(greatest_lower_bound(inverse(X1),X2),X1) = greatest_lower_bound(identity,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_177,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_165,c_0_31]) ).
cnf(c_0_178,plain,
least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),greatest_lower_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_166,c_0_39]) ).
cnf(c_0_179,plain,
least_upper_bound(identity,greatest_lower_bound(X1,least_upper_bound(X2,multiply(X1,X1)))) = least_upper_bound(X1,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_141]),c_0_21]) ).
cnf(c_0_180,plain,
least_upper_bound(multiply(X1,X2),multiply(greatest_lower_bound(X3,X1),greatest_lower_bound(X2,X4))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_168,c_0_25]) ).
cnf(c_0_181,plain,
multiply(least_upper_bound(X1,greatest_lower_bound(multiply(X2,X1),X3)),inverse(X1)) = least_upper_bound(identity,greatest_lower_bound(X2,multiply(X3,inverse(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_90]),c_0_22]) ).
cnf(c_0_182,plain,
greatest_lower_bound(multiply(X1,least_upper_bound(identity,X1)),multiply(X2,X1)) = multiply(greatest_lower_bound(least_upper_bound(identity,X1),X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_82]) ).
cnf(c_0_183,plain,
least_upper_bound(X1,greatest_lower_bound(least_upper_bound(X1,X2),X3)) = least_upper_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,X3))),
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_171]),c_0_172]),c_0_170]),c_0_171]) ).
cnf(c_0_184,plain,
least_upper_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(X1,X2)),X1)) = multiply(least_upper_bound(identity,greatest_lower_bound(X1,X2)),least_upper_bound(X1,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(spm,[status(thm)],[c_0_173,c_0_174]),c_0_135]),c_0_136]),c_0_31]),c_0_135]),c_0_136]),c_0_31]) ).
cnf(c_0_185,plain,
multiply(least_upper_bound(X1,identity),greatest_lower_bound(identity,inverse(X1))) = identity,
inference(rw,[status(thm)],[c_0_175,c_0_109]) ).
cnf(c_0_186,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_39,c_0_23]),c_0_26]) ).
cnf(c_0_187,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_29,c_0_15]),c_0_26]) ).
cnf(c_0_188,plain,
multiply(inverse(least_upper_bound(X1,X2)),X1) = greatest_lower_bound(identity,multiply(inverse(X2),X1)),
inference(spm,[status(thm)],[c_0_176,c_0_137]) ).
cnf(c_0_189,plain,
inverse(least_upper_bound(X1,identity)) = greatest_lower_bound(identity,inverse(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_109,c_0_59]),c_0_17]),c_0_67]),c_0_17]),c_0_109]),c_0_153]) ).
cnf(c_0_190,plain,
multiply(least_upper_bound(X1,inverse(multiply(X2,X3))),X2) = least_upper_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_61,c_0_32]) ).
cnf(c_0_191,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = inverse(greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[c_0_177,c_0_78]) ).
cnf(c_0_192,plain,
least_upper_bound(X1,least_upper_bound(X2,multiply(greatest_lower_bound(identity,X3),X1))) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_48]),c_0_46]) ).
cnf(c_0_193,plain,
least_upper_bound(identity,greatest_lower_bound(X1,multiply(X2,greatest_lower_bound(X1,identity)))) = least_upper_bound(identity,greatest_lower_bound(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_36]),c_0_47]),c_0_31]) ).
cnf(c_0_194,plain,
least_upper_bound(identity,greatest_lower_bound(X1,multiply(X2,greatest_lower_bound(identity,X1)))) = least_upper_bound(identity,greatest_lower_bound(X1,least_upper_bound(identity,X2))),
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_181,c_0_182]),c_0_46]),c_0_66]),c_0_31]),c_0_183]),c_0_184]),c_0_109]),c_0_15]),c_0_185]),c_0_21]),c_0_109]),c_0_15]),c_0_186]),c_0_21]) ).
cnf(c_0_195,plain,
multiply(greatest_lower_bound(identity,multiply(X1,X2)),X1) = multiply(X1,greatest_lower_bound(identity,multiply(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_187]),c_0_26]) ).
cnf(c_0_196,plain,
greatest_lower_bound(identity,multiply(least_upper_bound(identity,greatest_lower_bound(X1,X2)),X1)) = greatest_lower_bound(identity,X1),
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_188,c_0_174]),c_0_189]),c_0_35]),c_0_17]),c_0_135]),c_0_136]),c_0_31]) ).
cnf(c_0_197,plain,
greatest_lower_bound(identity,multiply(X1,least_upper_bound(identity,greatest_lower_bound(X1,X2)))) = greatest_lower_bound(identity,X1),
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_152,c_0_174]),c_0_189]),c_0_186]),c_0_21]),c_0_135]),c_0_136]),c_0_31]) ).
cnf(c_0_198,plain,
multiply(least_upper_bound(X1,greatest_lower_bound(identity,X2)),least_upper_bound(identity,X2)) = least_upper_bound(X2,multiply(X1,least_upper_bound(identity,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_22]),c_0_22]),c_0_31]) ).
cnf(c_0_199,plain,
least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),least_upper_bound(X3,X1))) = least_upper_bound(X1,multiply(greatest_lower_bound(identity,X2),X3)),
inference(spm,[status(thm)],[c_0_192,c_0_30]) ).
cnf(c_0_200,plain,
multiply(least_upper_bound(X1,X2),greatest_lower_bound(identity,multiply(inverse(X1),X2))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_158]),c_0_22]) ).
cnf(c_0_201,plain,
least_upper_bound(identity,greatest_lower_bound(X1,least_upper_bound(identity,X2))) = least_upper_bound(identity,greatest_lower_bound(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_26]),c_0_194]) ).
cnf(c_0_202,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,X3))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_74,c_0_26]) ).
cnf(c_0_203,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(X1,X2)),greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,greatest_lower_bound(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_197]) ).
cnf(c_0_204,plain,
multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,greatest_lower_bound(X1,X2))) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_97]),c_0_199]),c_0_21]) ).
cnf(c_0_205,plain,
multiply(X1,least_upper_bound(X2,greatest_lower_bound(X3,multiply(inverse(X1),X4)))) = least_upper_bound(multiply(X1,X2),greatest_lower_bound(multiply(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_30,c_0_68]) ).
cnf(c_0_206,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(identity,X1)) = greatest_lower_bound(X1,least_upper_bound(identity,X2)),
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_200,c_0_201]),c_0_136]),c_0_17]),c_0_202]),c_0_203]),c_0_204]) ).
cnf(c_0_207,plain,
multiply(X1,greatest_lower_bound(multiply(inverse(X1),X2),X3)) = greatest_lower_bound(X2,multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_39,c_0_28]) ).
cnf(c_0_208,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(X2,multiply(X1,least_upper_bound(identity,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_207]),c_0_207]),c_0_21]),c_0_31]) ).
cnf(c_0_209,plain,
multiply(X1,least_upper_bound(X2,multiply(inverse(X1),X3))) = least_upper_bound(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_210,negated_conjecture,
least_upper_bound(a,greatest_lower_bound(b,c)) != greatest_lower_bound(least_upper_bound(a,b),least_upper_bound(a,c)),
prove_distrnu ).
cnf(c_0_211,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,least_upper_bound(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_28]),c_0_209]),c_0_21]) ).
cnf(c_0_212,negated_conjecture,
least_upper_bound(a,greatest_lower_bound(b,least_upper_bound(a,c))) != least_upper_bound(a,greatest_lower_bound(b,c)),
inference(rw,[status(thm)],[c_0_210,c_0_171]) ).
cnf(c_0_213,plain,
least_upper_bound(X1,greatest_lower_bound(X2,least_upper_bound(X1,X3))) = least_upper_bound(X1,greatest_lower_bound(X2,X3)),
inference(spm,[status(thm)],[c_0_81,c_0_211]) ).
cnf(c_0_214,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_212,c_0_213])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP164-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.35 % Computer : n008.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon Aug 28 22:11:02 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 119.22/119.22 % Version : CSE_E---1.5
% 119.22/119.22 % Problem : theBenchmark.p
% 119.22/119.22 % Proof found
% 119.22/119.22 % SZS status Theorem for theBenchmark.p
% 119.22/119.22 % SZS output start Proof
% See solution above
% 119.22/119.24 % Total time : 118.628000 s
% 119.22/119.24 % SZS output end Proof
% 119.22/119.24 % Total time : 118.636000 s
%------------------------------------------------------------------------------