TSTP Solution File: GRP178-1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GRP178-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:21:36 EDT 2024
% Result : Timeout 295.66s 38.19s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 20
% Syntax : Number of clauses : 360 ( 360 unt; 0 nHn; 148 RR)
% Number of literals : 360 ( 359 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% 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 : 276 ( 47 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_49,plain,
least_upper_bound(identity,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p09a_1) ).
cnf(c_50,plain,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p09a_2) ).
cnf(c_51,plain,
least_upper_bound(identity,c) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p09a_3) ).
cnf(c_52,plain,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p09a_4) ).
cnf(c_53,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p09a) ).
cnf(c_54,plain,
greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(c_55,plain,
least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(c_56,plain,
greatest_lower_bound(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(X0,greatest_lower_bound(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(c_57,plain,
least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X0,least_upper_bound(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
cnf(c_58,plain,
least_upper_bound(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
cnf(c_59,plain,
greatest_lower_bound(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(c_60,plain,
least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(c_61,plain,
greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(c_62,plain,
least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,least_upper_bound(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(c_63,plain,
greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,greatest_lower_bound(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(c_64,plain,
least_upper_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(least_upper_bound(X0,X2),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(c_65,plain,
greatest_lower_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(greatest_lower_bound(X0,X2),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(c_66,plain,
multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(c_67,plain,
multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(c_68,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(c_202,plain,
least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,X2)),
inference(superposition,[status(thm)],[c_57,c_55]) ).
cnf(c_203,plain,
greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2)),
inference(superposition,[status(thm)],[c_56,c_54]) ).
cnf(c_209,plain,
least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_54,c_60]) ).
cnf(c_213,plain,
greatest_lower_bound(identity,a) = identity,
inference(superposition,[status(thm)],[c_49,c_61]) ).
cnf(c_214,plain,
greatest_lower_bound(identity,b) = identity,
inference(superposition,[status(thm)],[c_50,c_61]) ).
cnf(c_215,plain,
greatest_lower_bound(identity,c) = identity,
inference(superposition,[status(thm)],[c_51,c_61]) ).
cnf(c_216,plain,
greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_55,c_61]) ).
cnf(c_223,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X0)) = greatest_lower_bound(identity,X0),
inference(superposition,[status(thm)],[c_52,c_56]) ).
cnf(c_235,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,X0)) = greatest_lower_bound(identity,X0),
inference(superposition,[status(thm)],[c_213,c_56]) ).
cnf(c_241,plain,
greatest_lower_bound(identity,greatest_lower_bound(c,X0)) = greatest_lower_bound(identity,X0),
inference(superposition,[status(thm)],[c_215,c_56]) ).
cnf(c_247,plain,
least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0))) = X0,
inference(superposition,[status(thm)],[c_56,c_209]) ).
cnf(c_284,plain,
least_upper_bound(X0,least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
inference(superposition,[status(thm)],[c_58,c_57]) ).
cnf(c_285,plain,
least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X0,X1),X2)) = least_upper_bound(X0,X2),
inference(superposition,[status(thm)],[c_60,c_57]) ).
cnf(c_286,plain,
least_upper_bound(X0,least_upper_bound(greatest_lower_bound(X1,X0),X2)) = least_upper_bound(X0,X2),
inference(superposition,[status(thm)],[c_209,c_57]) ).
cnf(c_288,plain,
greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) = X0,
inference(superposition,[status(thm)],[c_57,c_216]) ).
cnf(c_302,plain,
multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_67,c_68]) ).
cnf(c_352,plain,
greatest_lower_bound(a,greatest_lower_bound(X0,b)) = greatest_lower_bound(identity,X0),
inference(superposition,[status(thm)],[c_54,c_223]) ).
cnf(c_355,plain,
greatest_lower_bound(identity,least_upper_bound(b,X0)) = greatest_lower_bound(a,b),
inference(superposition,[status(thm)],[c_61,c_223]) ).
cnf(c_356,plain,
greatest_lower_bound(identity,least_upper_bound(X0,b)) = greatest_lower_bound(a,b),
inference(superposition,[status(thm)],[c_216,c_223]) ).
cnf(c_358,plain,
least_upper_bound(a,greatest_lower_bound(identity,X0)) = a,
inference(superposition,[status(thm)],[c_223,c_60]) ).
cnf(c_359,plain,
least_upper_bound(greatest_lower_bound(b,X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(b,X0),
inference(superposition,[status(thm)],[c_223,c_209]) ).
cnf(c_361,plain,
greatest_lower_bound(identity,least_upper_bound(X0,b)) = identity,
inference(light_normalisation,[status(thm)],[c_356,c_52]) ).
cnf(c_362,plain,
greatest_lower_bound(identity,least_upper_bound(b,X0)) = identity,
inference(light_normalisation,[status(thm)],[c_355,c_52]) ).
cnf(c_363,plain,
least_upper_bound(greatest_lower_bound(identity,X0),greatest_lower_bound(b,X0)) = greatest_lower_bound(b,X0),
inference(theory_normalisation,[status(thm)],[c_359,c_57,c_55,c_56,c_54]) ).
cnf(c_388,plain,
greatest_lower_bound(identity,least_upper_bound(X0,least_upper_bound(X1,b))) = identity,
inference(superposition,[status(thm)],[c_57,c_361]) ).
cnf(c_406,plain,
least_upper_bound(least_upper_bound(b,X0),identity) = least_upper_bound(b,X0),
inference(superposition,[status(thm)],[c_362,c_209]) ).
cnf(c_409,plain,
least_upper_bound(identity,least_upper_bound(X0,b)) = least_upper_bound(b,X0),
inference(theory_normalisation,[status(thm)],[c_406,c_57,c_55,c_56,c_54]) ).
cnf(c_427,plain,
least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_66,c_64]) ).
cnf(c_430,plain,
least_upper_bound(multiply(X0,X1),X1) = multiply(least_upper_bound(X0,identity),X1),
inference(superposition,[status(thm)],[c_66,c_64]) ).
cnf(c_443,plain,
least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(X1,identity),X0),
inference(theory_normalisation,[status(thm)],[c_430,c_57,c_55,c_56,c_54]) ).
cnf(c_457,plain,
greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_66,c_65]) ).
cnf(c_460,plain,
greatest_lower_bound(multiply(X0,X1),X1) = multiply(greatest_lower_bound(X0,identity),X1),
inference(superposition,[status(thm)],[c_66,c_65]) ).
cnf(c_473,plain,
greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(X1,identity),X0),
inference(theory_normalisation,[status(thm)],[c_460,c_57,c_55,c_56,c_54]) ).
cnf(c_517,plain,
greatest_lower_bound(identity,least_upper_bound(a,X0)) = greatest_lower_bound(identity,a),
inference(superposition,[status(thm)],[c_61,c_235]) ).
cnf(c_527,plain,
greatest_lower_bound(identity,least_upper_bound(a,X0)) = identity,
inference(light_normalisation,[status(thm)],[c_517,c_213]) ).
cnf(c_559,plain,
least_upper_bound(least_upper_bound(a,X0),identity) = least_upper_bound(a,X0),
inference(superposition,[status(thm)],[c_527,c_209]) ).
cnf(c_562,plain,
least_upper_bound(identity,least_upper_bound(X0,a)) = least_upper_bound(a,X0),
inference(theory_normalisation,[status(thm)],[c_559,c_57,c_55,c_56,c_54]) ).
cnf(c_581,plain,
greatest_lower_bound(identity,least_upper_bound(c,X0)) = greatest_lower_bound(identity,c),
inference(superposition,[status(thm)],[c_61,c_241]) ).
cnf(c_589,plain,
greatest_lower_bound(identity,least_upper_bound(c,X0)) = identity,
inference(light_normalisation,[status(thm)],[c_581,c_215]) ).
cnf(c_619,plain,
least_upper_bound(least_upper_bound(c,X0),identity) = least_upper_bound(c,X0),
inference(superposition,[status(thm)],[c_589,c_209]) ).
cnf(c_622,plain,
least_upper_bound(identity,least_upper_bound(X0,c)) = least_upper_bound(c,X0),
inference(theory_normalisation,[status(thm)],[c_619,c_57,c_55,c_56,c_54]) ).
cnf(c_640,plain,
least_upper_bound(least_upper_bound(X0,X1),greatest_lower_bound(X2,X0)) = least_upper_bound(X0,X1),
inference(superposition,[status(thm)],[c_61,c_247]) ).
cnf(c_645,plain,
least_upper_bound(b,greatest_lower_bound(X0,identity)) = b,
inference(superposition,[status(thm)],[c_214,c_247]) ).
cnf(c_646,plain,
least_upper_bound(c,greatest_lower_bound(X0,identity)) = c,
inference(superposition,[status(thm)],[c_215,c_247]) ).
cnf(c_673,plain,
least_upper_bound(X0,least_upper_bound(X1,greatest_lower_bound(X2,X0))) = least_upper_bound(X0,X1),
inference(theory_normalisation,[status(thm)],[c_640,c_57,c_55,c_56,c_54]) ).
cnf(c_693,plain,
least_upper_bound(b,greatest_lower_bound(identity,X0)) = b,
inference(superposition,[status(thm)],[c_54,c_645]) ).
cnf(c_706,plain,
least_upper_bound(c,greatest_lower_bound(identity,X0)) = c,
inference(superposition,[status(thm)],[c_54,c_646]) ).
cnf(c_852,plain,
greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_55,c_288]) ).
cnf(c_856,plain,
greatest_lower_bound(greatest_lower_bound(X0,X1),least_upper_bound(X2,X0)) = greatest_lower_bound(X0,X1),
inference(superposition,[status(thm)],[c_60,c_288]) ).
cnf(c_899,plain,
greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(X2,X0))) = greatest_lower_bound(X0,X1),
inference(theory_normalisation,[status(thm)],[c_856,c_57,c_55,c_56,c_54]) ).
cnf(c_953,plain,
greatest_lower_bound(identity,least_upper_bound(X0,least_upper_bound(X1,least_upper_bound(X2,b)))) = identity,
inference(superposition,[status(thm)],[c_57,c_388]) ).
cnf(c_1743,plain,
multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_66,c_302]) ).
cnf(c_1744,plain,
multiply(inverse(inverse(X0)),identity) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_67,c_302]) ).
cnf(c_1757,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(light_normalisation,[status(thm)],[c_1744,c_66]) ).
cnf(c_1776,plain,
multiply(inverse(inverse(identity)),X0) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1743,c_302]) ).
cnf(c_1786,plain,
multiply(inverse(inverse(identity)),X0) = X0,
inference(light_normalisation,[status(thm)],[c_1776,c_66]) ).
cnf(c_1798,plain,
multiply(inverse(inverse(X0)),multiply(identity,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_1757,c_68]) ).
cnf(c_2041,plain,
greatest_lower_bound(identity,greatest_lower_bound(X0,a)) = greatest_lower_bound(X0,identity),
inference(superposition,[status(thm)],[c_213,c_203]) ).
cnf(c_2218,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_1786,c_67]) ).
cnf(c_2243,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,X0)) = greatest_lower_bound(X0,identity),
inference(superposition,[status(thm)],[c_54,c_2041]) ).
cnf(c_2415,plain,
greatest_lower_bound(greatest_lower_bound(X0,b),identity) = greatest_lower_bound(identity,greatest_lower_bound(identity,X0)),
inference(superposition,[status(thm)],[c_352,c_2243]) ).
cnf(c_2461,plain,
greatest_lower_bound(X0,greatest_lower_bound(identity,b)) = greatest_lower_bound(identity,greatest_lower_bound(identity,X0)),
inference(theory_normalisation,[status(thm)],[c_2415,c_57,c_55,c_56,c_54]) ).
cnf(c_2462,plain,
greatest_lower_bound(identity,greatest_lower_bound(identity,X0)) = greatest_lower_bound(X0,identity),
inference(light_normalisation,[status(thm)],[c_2461,c_214]) ).
cnf(c_3168,plain,
least_upper_bound(X0,least_upper_bound(X1,greatest_lower_bound(X0,X2))) = least_upper_bound(X0,X1),
inference(superposition,[status(thm)],[c_55,c_285]) ).
cnf(c_3844,plain,
least_upper_bound(identity,greatest_lower_bound(b,c)) = greatest_lower_bound(b,c),
inference(superposition,[status(thm)],[c_215,c_363]) ).
cnf(c_4036,plain,
greatest_lower_bound(identity,least_upper_bound(X0,greatest_lower_bound(b,c))) = identity,
inference(superposition,[status(thm)],[c_3844,c_852]) ).
cnf(c_4098,plain,
multiply(least_upper_bound(identity,inverse(X0)),X0) = least_upper_bound(X0,identity),
inference(superposition,[status(thm)],[c_67,c_427]) ).
cnf(c_4156,plain,
multiply(least_upper_bound(identity,identity),identity) = least_upper_bound(identity,identity),
inference(superposition,[status(thm)],[c_2218,c_4098]) ).
cnf(c_4747,plain,
least_upper_bound(c,multiply(greatest_lower_bound(identity,X0),identity)) = c,
inference(superposition,[status(thm)],[c_457,c_706]) ).
cnf(c_4748,plain,
least_upper_bound(b,multiply(greatest_lower_bound(identity,X0),identity)) = b,
inference(superposition,[status(thm)],[c_457,c_693]) ).
cnf(c_4749,plain,
least_upper_bound(a,multiply(greatest_lower_bound(identity,X0),identity)) = a,
inference(superposition,[status(thm)],[c_457,c_358]) ).
cnf(c_5234,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(identity,identity)),identity) = greatest_lower_bound(identity,least_upper_bound(identity,identity)),
inference(superposition,[status(thm)],[c_4156,c_457]) ).
cnf(c_8943,plain,
least_upper_bound(c,multiply(identity,identity)) = c,
inference(superposition,[status(thm)],[c_953,c_4747]) ).
cnf(c_9020,plain,
greatest_lower_bound(multiply(identity,identity),c) = multiply(identity,identity),
inference(superposition,[status(thm)],[c_8943,c_216]) ).
cnf(c_9034,plain,
greatest_lower_bound(c,multiply(identity,identity)) = multiply(identity,identity),
inference(theory_normalisation,[status(thm)],[c_9020,c_57,c_55,c_56,c_54]) ).
cnf(c_9090,plain,
least_upper_bound(b,multiply(identity,identity)) = b,
inference(superposition,[status(thm)],[c_953,c_4748]) ).
cnf(c_9764,plain,
greatest_lower_bound(multiply(identity,identity),b) = multiply(identity,identity),
inference(superposition,[status(thm)],[c_9090,c_216]) ).
cnf(c_9780,plain,
greatest_lower_bound(b,multiply(identity,identity)) = multiply(identity,identity),
inference(theory_normalisation,[status(thm)],[c_9764,c_57,c_55,c_56,c_54]) ).
cnf(c_9836,plain,
least_upper_bound(a,multiply(identity,identity)) = a,
inference(superposition,[status(thm)],[c_953,c_4749]) ).
cnf(c_9916,plain,
greatest_lower_bound(multiply(identity,identity),a) = multiply(identity,identity),
inference(superposition,[status(thm)],[c_9836,c_216]) ).
cnf(c_9931,plain,
greatest_lower_bound(a,multiply(identity,identity)) = multiply(identity,identity),
inference(theory_normalisation,[status(thm)],[c_9916,c_57,c_55,c_56,c_54]) ).
cnf(c_10934,plain,
multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_66,c_1798]) ).
cnf(c_10954,plain,
multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_1757,c_10934]) ).
cnf(c_10989,plain,
greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(identity,X1)),
inference(superposition,[status(thm)],[c_10954,c_63]) ).
cnf(c_10990,plain,
least_upper_bound(X0,multiply(X0,X1)) = multiply(X0,least_upper_bound(identity,X1)),
inference(superposition,[status(thm)],[c_10954,c_62]) ).
cnf(c_10992,plain,
greatest_lower_bound(multiply(X0,X1),X0) = multiply(X0,greatest_lower_bound(X1,identity)),
inference(superposition,[status(thm)],[c_10954,c_63]) ).
cnf(c_10993,plain,
least_upper_bound(multiply(X0,X1),X0) = multiply(X0,least_upper_bound(X1,identity)),
inference(superposition,[status(thm)],[c_10954,c_62]) ).
cnf(c_10994,plain,
multiply(greatest_lower_bound(X0,identity),identity) = greatest_lower_bound(identity,X0),
inference(superposition,[status(thm)],[c_10954,c_473]) ).
cnf(c_10996,plain,
multiply(least_upper_bound(X0,identity),identity) = least_upper_bound(identity,X0),
inference(superposition,[status(thm)],[c_10954,c_443]) ).
cnf(c_11011,plain,
least_upper_bound(X0,multiply(X0,X1)) = multiply(X0,least_upper_bound(X1,identity)),
inference(theory_normalisation,[status(thm)],[c_10993,c_57,c_55,c_56,c_54]) ).
cnf(c_11012,plain,
greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(X1,identity)),
inference(theory_normalisation,[status(thm)],[c_10992,c_57,c_55,c_56,c_54]) ).
cnf(c_11040,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_10934,c_67]) ).
cnf(c_11085,plain,
multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_11040,c_68]) ).
cnf(c_11686,plain,
least_upper_bound(identity,least_upper_bound(X0,identity)) = least_upper_bound(identity,X0),
inference(superposition,[status(thm)],[c_4036,c_3168]) ).
cnf(c_15713,plain,
least_upper_bound(c,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(c,X0),
inference(superposition,[status(thm)],[c_9034,c_3168]) ).
cnf(c_15736,plain,
least_upper_bound(b,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(b,X0),
inference(superposition,[status(thm)],[c_9780,c_3168]) ).
cnf(c_15744,plain,
greatest_lower_bound(identity,multiply(identity,identity)) = greatest_lower_bound(a,multiply(identity,identity)),
inference(superposition,[status(thm)],[c_9780,c_223]) ).
cnf(c_15748,plain,
greatest_lower_bound(identity,multiply(identity,identity)) = multiply(identity,identity),
inference(light_normalisation,[status(thm)],[c_15744,c_9931]) ).
cnf(c_15765,plain,
least_upper_bound(a,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(a,X0),
inference(superposition,[status(thm)],[c_9931,c_3168]) ).
cnf(c_16155,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X0,identity),identity),identity) = greatest_lower_bound(identity,greatest_lower_bound(identity,X0)),
inference(superposition,[status(thm)],[c_10994,c_473]) ).
cnf(c_16164,plain,
multiply(greatest_lower_bound(X0,greatest_lower_bound(identity,identity)),identity) = greatest_lower_bound(identity,greatest_lower_bound(identity,X0)),
inference(theory_normalisation,[status(thm)],[c_16155,c_57,c_55,c_56,c_54]) ).
cnf(c_16165,plain,
multiply(greatest_lower_bound(X0,greatest_lower_bound(identity,identity)),identity) = greatest_lower_bound(X0,identity),
inference(light_normalisation,[status(thm)],[c_16164,c_2462]) ).
cnf(c_16201,plain,
multiply(least_upper_bound(identity,least_upper_bound(X0,identity)),identity) = least_upper_bound(identity,least_upper_bound(identity,X0)),
inference(superposition,[status(thm)],[c_10996,c_427]) ).
cnf(c_16205,plain,
least_upper_bound(identity,least_upper_bound(identity,X0)) = multiply(least_upper_bound(identity,X0),identity),
inference(light_normalisation,[status(thm)],[c_16201,c_11686]) ).
cnf(c_17527,plain,
least_upper_bound(X0,least_upper_bound(identity,identity)) = least_upper_bound(identity,X0),
inference(superposition,[status(thm)],[c_11686,c_202]) ).
cnf(c_17532,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X0)) = least_upper_bound(identity,identity),
inference(superposition,[status(thm)],[c_11686,c_285]) ).
cnf(c_17533,plain,
least_upper_bound(identity,greatest_lower_bound(X0,identity)) = least_upper_bound(identity,identity),
inference(superposition,[status(thm)],[c_11686,c_286]) ).
cnf(c_18645,plain,
least_upper_bound(identity,multiply(identity,identity)) = identity,
inference(superposition,[status(thm)],[c_15748,c_60]) ).
cnf(c_18666,plain,
multiply(greatest_lower_bound(identity,identity),identity) = multiply(identity,identity),
inference(superposition,[status(thm)],[c_15748,c_473]) ).
cnf(c_18693,plain,
least_upper_bound(identity,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(X0,identity),
inference(superposition,[status(thm)],[c_18645,c_202]) ).
cnf(c_18700,plain,
multiply(least_upper_bound(identity,identity),identity) = identity,
inference(superposition,[status(thm)],[c_18645,c_443]) ).
cnf(c_18714,plain,
multiply(least_upper_bound(identity,identity),multiply(identity,inverse(identity))) = identity,
inference(superposition,[status(thm)],[c_18700,c_11085]) ).
cnf(c_18723,plain,
multiply(greatest_lower_bound(least_upper_bound(identity,identity),identity),identity) = greatest_lower_bound(identity,identity),
inference(superposition,[status(thm)],[c_18700,c_473]) ).
cnf(c_18731,plain,
multiply(least_upper_bound(identity,identity),multiply(identity,identity)) = identity,
inference(light_normalisation,[status(thm)],[c_18714,c_2218]) ).
cnf(c_18734,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(identity,identity)),identity) = greatest_lower_bound(identity,identity),
inference(theory_normalisation,[status(thm)],[c_18723,c_57,c_55,c_56,c_54]) ).
cnf(c_18735,plain,
greatest_lower_bound(identity,least_upper_bound(identity,identity)) = greatest_lower_bound(identity,identity),
inference(light_normalisation,[status(thm)],[c_18734,c_5234]) ).
cnf(c_20006,plain,
greatest_lower_bound(multiply(X0,identity),multiply(identity,identity)) = multiply(greatest_lower_bound(X0,greatest_lower_bound(identity,identity)),identity),
inference(superposition,[status(thm)],[c_18666,c_65]) ).
cnf(c_20008,plain,
greatest_lower_bound(identity,identity) = multiply(identity,identity),
inference(superposition,[status(thm)],[c_18666,c_10954]) ).
cnf(c_20018,plain,
greatest_lower_bound(X0,multiply(identity,identity)) = greatest_lower_bound(X0,identity),
inference(light_normalisation,[status(thm)],[c_20006,c_10954,c_16165]) ).
cnf(c_20594,plain,
multiply(identity,multiply(identity,identity)) = identity,
inference(superposition,[status(thm)],[c_58,c_18731]) ).
cnf(c_20607,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(identity,identity)),multiply(identity,identity)) = greatest_lower_bound(multiply(identity,identity),identity),
inference(superposition,[status(thm)],[c_18731,c_457]) ).
cnf(c_20619,plain,
multiply(greatest_lower_bound(identity,least_upper_bound(identity,identity)),multiply(identity,identity)) = greatest_lower_bound(identity,multiply(identity,identity)),
inference(theory_normalisation,[status(thm)],[c_20607,c_57,c_55,c_56,c_54]) ).
cnf(c_20620,plain,
multiply(multiply(identity,identity),multiply(identity,identity)) = greatest_lower_bound(identity,multiply(identity,identity)),
inference(light_normalisation,[status(thm)],[c_20619,c_18735,c_20008]) ).
cnf(c_20642,plain,
multiply(identity,multiply(multiply(identity,identity),inverse(identity))) = identity,
inference(superposition,[status(thm)],[c_20594,c_11085]) ).
cnf(c_20649,plain,
multiply(identity,greatest_lower_bound(X0,multiply(identity,identity))) = greatest_lower_bound(multiply(identity,X0),identity),
inference(superposition,[status(thm)],[c_20594,c_63]) ).
cnf(c_20658,plain,
multiply(identity,multiply(multiply(identity,identity),identity)) = identity,
inference(light_normalisation,[status(thm)],[c_20642,c_2218]) ).
cnf(c_20666,plain,
multiply(identity,greatest_lower_bound(X0,multiply(identity,identity))) = greatest_lower_bound(identity,multiply(identity,X0)),
inference(theory_normalisation,[status(thm)],[c_20649,c_57,c_55,c_56,c_54]) ).
cnf(c_20667,plain,
multiply(identity,greatest_lower_bound(X0,identity)) = greatest_lower_bound(identity,X0),
inference(light_normalisation,[status(thm)],[c_20666,c_66,c_20018]) ).
cnf(c_22357,plain,
multiply(multiply(identity,identity),identity) = identity,
inference(superposition,[status(thm)],[c_20658,c_66]) ).
cnf(c_22383,plain,
multiply(multiply(identity,identity),multiply(identity,inverse(identity))) = identity,
inference(superposition,[status(thm)],[c_22357,c_11085]) ).
cnf(c_22395,plain,
multiply(least_upper_bound(identity,multiply(identity,identity)),identity) = least_upper_bound(identity,identity),
inference(superposition,[status(thm)],[c_22357,c_427]) ).
cnf(c_22400,plain,
greatest_lower_bound(identity,multiply(identity,identity)) = identity,
inference(light_normalisation,[status(thm)],[c_22383,c_2218,c_20620]) ).
cnf(c_22401,plain,
least_upper_bound(identity,identity) = multiply(identity,identity),
inference(light_normalisation,[status(thm)],[c_22395,c_18645]) ).
cnf(c_22422,plain,
least_upper_bound(X0,multiply(identity,identity)) = least_upper_bound(identity,X0),
inference(demodulation,[status(thm)],[c_17527,c_22401]) ).
cnf(c_22446,plain,
least_upper_bound(multiply(identity,identity),least_upper_bound(X0,identity)) = least_upper_bound(multiply(identity,identity),X0),
inference(superposition,[status(thm)],[c_22400,c_673]) ).
cnf(c_22484,plain,
least_upper_bound(identity,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(multiply(identity,identity),X0),
inference(theory_normalisation,[status(thm)],[c_22446,c_57,c_55,c_56,c_54]) ).
cnf(c_22485,plain,
least_upper_bound(multiply(identity,identity),X0) = least_upper_bound(X0,identity),
inference(light_normalisation,[status(thm)],[c_22484,c_18693]) ).
cnf(c_23119,plain,
least_upper_bound(multiply(identity,identity),X0) = least_upper_bound(identity,least_upper_bound(identity,X0)),
inference(superposition,[status(thm)],[c_22401,c_57]) ).
cnf(c_23149,plain,
multiply(least_upper_bound(identity,X0),identity) = least_upper_bound(X0,identity),
inference(light_normalisation,[status(thm)],[c_23119,c_16205,c_22485]) ).
cnf(c_23896,plain,
least_upper_bound(multiply(identity,identity),X0) = least_upper_bound(identity,X0),
inference(superposition,[status(thm)],[c_22422,c_55]) ).
cnf(c_23900,plain,
least_upper_bound(identity,multiply(identity,X0)) = multiply(identity,least_upper_bound(X0,identity)),
inference(superposition,[status(thm)],[c_22422,c_62]) ).
cnf(c_23968,plain,
multiply(identity,least_upper_bound(X0,identity)) = least_upper_bound(identity,X0),
inference(light_normalisation,[status(thm)],[c_23900,c_66]) ).
cnf(c_24057,plain,
least_upper_bound(X0,multiply(identity,identity)) = least_upper_bound(X0,identity),
inference(superposition,[status(thm)],[c_22485,c_55]) ).
cnf(c_24840,plain,
least_upper_bound(least_upper_bound(X0,b),identity) = multiply(least_upper_bound(b,X0),identity),
inference(superposition,[status(thm)],[c_409,c_23149]) ).
cnf(c_24844,plain,
least_upper_bound(least_upper_bound(X0,a),identity) = multiply(least_upper_bound(a,X0),identity),
inference(superposition,[status(thm)],[c_562,c_23149]) ).
cnf(c_24846,plain,
least_upper_bound(least_upper_bound(X0,c),identity) = multiply(least_upper_bound(c,X0),identity),
inference(superposition,[status(thm)],[c_622,c_23149]) ).
cnf(c_24929,plain,
least_upper_bound(X0,least_upper_bound(identity,c)) = multiply(least_upper_bound(c,X0),identity),
inference(theory_normalisation,[status(thm)],[c_24846,c_57,c_55,c_56,c_54]) ).
cnf(c_24930,plain,
multiply(least_upper_bound(c,X0),identity) = least_upper_bound(X0,c),
inference(light_normalisation,[status(thm)],[c_24929,c_51]) ).
cnf(c_24933,plain,
least_upper_bound(X0,least_upper_bound(identity,a)) = multiply(least_upper_bound(a,X0),identity),
inference(theory_normalisation,[status(thm)],[c_24844,c_57,c_55,c_56,c_54]) ).
cnf(c_24934,plain,
multiply(least_upper_bound(a,X0),identity) = least_upper_bound(X0,a),
inference(light_normalisation,[status(thm)],[c_24933,c_49]) ).
cnf(c_24937,plain,
least_upper_bound(X0,least_upper_bound(identity,b)) = multiply(least_upper_bound(b,X0),identity),
inference(theory_normalisation,[status(thm)],[c_24840,c_57,c_55,c_56,c_54]) ).
cnf(c_24938,plain,
multiply(least_upper_bound(b,X0),identity) = least_upper_bound(X0,b),
inference(light_normalisation,[status(thm)],[c_24937,c_50]) ).
cnf(c_25579,plain,
least_upper_bound(greatest_lower_bound(X0,c),c) = multiply(c,identity),
inference(superposition,[status(thm)],[c_209,c_24930]) ).
cnf(c_25601,plain,
least_upper_bound(multiply(identity,identity),c) = multiply(least_upper_bound(identity,c),identity),
inference(superposition,[status(thm)],[c_22422,c_24930]) ).
cnf(c_25622,plain,
least_upper_bound(c,greatest_lower_bound(X0,c)) = multiply(c,identity),
inference(theory_normalisation,[status(thm)],[c_25579,c_57,c_55,c_56,c_54]) ).
cnf(c_25624,plain,
least_upper_bound(c,multiply(identity,identity)) = multiply(least_upper_bound(identity,c),identity),
inference(theory_normalisation,[status(thm)],[c_25601,c_57,c_55,c_56,c_54]) ).
cnf(c_25625,plain,
least_upper_bound(c,multiply(identity,identity)) = multiply(c,identity),
inference(light_normalisation,[status(thm)],[c_25624,c_51]) ).
cnf(c_25698,plain,
least_upper_bound(greatest_lower_bound(X0,a),a) = multiply(a,identity),
inference(superposition,[status(thm)],[c_209,c_24934]) ).
cnf(c_25721,plain,
least_upper_bound(multiply(identity,identity),a) = multiply(least_upper_bound(identity,a),identity),
inference(superposition,[status(thm)],[c_22422,c_24934]) ).
cnf(c_25742,plain,
least_upper_bound(a,greatest_lower_bound(X0,a)) = multiply(a,identity),
inference(theory_normalisation,[status(thm)],[c_25698,c_57,c_55,c_56,c_54]) ).
cnf(c_25744,plain,
least_upper_bound(a,multiply(identity,identity)) = multiply(least_upper_bound(identity,a),identity),
inference(theory_normalisation,[status(thm)],[c_25721,c_57,c_55,c_56,c_54]) ).
cnf(c_25745,plain,
least_upper_bound(a,multiply(identity,identity)) = multiply(a,identity),
inference(light_normalisation,[status(thm)],[c_25744,c_49]) ).
cnf(c_25843,plain,
least_upper_bound(multiply(identity,identity),b) = multiply(least_upper_bound(identity,b),identity),
inference(superposition,[status(thm)],[c_22422,c_24938]) ).
cnf(c_25866,plain,
least_upper_bound(b,multiply(identity,identity)) = multiply(least_upper_bound(identity,b),identity),
inference(theory_normalisation,[status(thm)],[c_25843,c_57,c_55,c_56,c_54]) ).
cnf(c_25867,plain,
least_upper_bound(b,multiply(identity,identity)) = multiply(b,identity),
inference(light_normalisation,[status(thm)],[c_25866,c_50]) ).
cnf(c_26391,plain,
greatest_lower_bound(c,multiply(c,identity)) = c,
inference(superposition,[status(thm)],[c_25625,c_61]) ).
cnf(c_26396,plain,
least_upper_bound(c,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(X0,multiply(c,identity)),
inference(superposition,[status(thm)],[c_25625,c_202]) ).
cnf(c_26427,plain,
least_upper_bound(X0,multiply(c,identity)) = least_upper_bound(c,X0),
inference(light_normalisation,[status(thm)],[c_26396,c_15713]) ).
cnf(c_26482,plain,
least_upper_bound(c,least_upper_bound(X0,c)) = least_upper_bound(c,X0),
inference(superposition,[status(thm)],[c_26391,c_3168]) ).
cnf(c_26836,plain,
greatest_lower_bound(a,multiply(a,identity)) = a,
inference(superposition,[status(thm)],[c_25745,c_61]) ).
cnf(c_26841,plain,
least_upper_bound(a,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(X0,multiply(a,identity)),
inference(superposition,[status(thm)],[c_25745,c_202]) ).
cnf(c_26872,plain,
least_upper_bound(X0,multiply(a,identity)) = least_upper_bound(a,X0),
inference(light_normalisation,[status(thm)],[c_26841,c_15765]) ).
cnf(c_26899,plain,
least_upper_bound(a,least_upper_bound(X0,a)) = least_upper_bound(a,X0),
inference(superposition,[status(thm)],[c_26836,c_3168]) ).
cnf(c_26900,plain,
greatest_lower_bound(a,greatest_lower_bound(X0,multiply(a,identity))) = greatest_lower_bound(X0,a),
inference(superposition,[status(thm)],[c_26836,c_203]) ).
cnf(c_26993,plain,
least_upper_bound(b,multiply(b,identity)) = multiply(b,identity),
inference(superposition,[status(thm)],[c_25867,c_284]) ).
cnf(c_26995,plain,
greatest_lower_bound(b,multiply(b,identity)) = b,
inference(superposition,[status(thm)],[c_25867,c_61]) ).
cnf(c_27000,plain,
least_upper_bound(b,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(X0,multiply(b,identity)),
inference(superposition,[status(thm)],[c_25867,c_202]) ).
cnf(c_27031,plain,
least_upper_bound(X0,multiply(b,identity)) = least_upper_bound(b,X0),
inference(light_normalisation,[status(thm)],[c_27000,c_15736]) ).
cnf(c_27059,plain,
greatest_lower_bound(b,greatest_lower_bound(X0,multiply(b,identity))) = greatest_lower_bound(X0,b),
inference(superposition,[status(thm)],[c_26995,c_203]) ).
cnf(c_27749,plain,
multiply(a,greatest_lower_bound(identity,identity)) = a,
inference(demodulation,[status(thm)],[c_26836,c_10989]) ).
cnf(c_27750,plain,
multiply(b,greatest_lower_bound(identity,identity)) = b,
inference(demodulation,[status(thm)],[c_26995,c_10989]) ).
cnf(c_27751,plain,
multiply(c,greatest_lower_bound(identity,identity)) = c,
inference(demodulation,[status(thm)],[c_26391,c_10989]) ).
cnf(c_27752,plain,
multiply(c,multiply(identity,identity)) = c,
inference(light_normalisation,[status(thm)],[c_27751,c_20008]) ).
cnf(c_27753,plain,
multiply(b,multiply(identity,identity)) = b,
inference(light_normalisation,[status(thm)],[c_27750,c_20008]) ).
cnf(c_27754,plain,
multiply(a,multiply(identity,identity)) = a,
inference(light_normalisation,[status(thm)],[c_27749,c_20008]) ).
cnf(c_27780,plain,
multiply(X0,greatest_lower_bound(identity,identity)) = greatest_lower_bound(X0,X0),
inference(superposition,[status(thm)],[c_10954,c_10989]) ).
cnf(c_27861,plain,
multiply(X0,multiply(identity,identity)) = X0,
inference(light_normalisation,[status(thm)],[c_27780,c_59,c_20008]) ).
cnf(c_28019,plain,
multiply(b,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(multiply(b,X0),b),
inference(superposition,[status(thm)],[c_27753,c_62]) ).
cnf(c_28025,plain,
least_upper_bound(multiply(X0,multiply(identity,identity)),b) = multiply(least_upper_bound(X0,b),multiply(identity,identity)),
inference(superposition,[status(thm)],[c_27753,c_64]) ).
cnf(c_28035,plain,
multiply(b,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(b,multiply(b,X0)),
inference(theory_normalisation,[status(thm)],[c_28019,c_57,c_55,c_56,c_54]) ).
cnf(c_28036,plain,
least_upper_bound(b,multiply(b,X0)) = multiply(b,least_upper_bound(X0,identity)),
inference(light_normalisation,[status(thm)],[c_28035,c_24057]) ).
cnf(c_28041,plain,
least_upper_bound(b,multiply(X0,multiply(identity,identity))) = multiply(least_upper_bound(X0,b),multiply(identity,identity)),
inference(theory_normalisation,[status(thm)],[c_28025,c_57,c_55,c_56,c_54]) ).
cnf(c_28042,plain,
multiply(least_upper_bound(X0,b),multiply(identity,identity)) = least_upper_bound(b,X0),
inference(light_normalisation,[status(thm)],[c_28041,c_27861]) ).
cnf(c_28070,plain,
multiply(identity,multiply(identity,identity)) = multiply(inverse(a),a),
inference(superposition,[status(thm)],[c_27754,c_302]) ).
cnf(c_28077,plain,
multiply(a,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(multiply(a,X0),a),
inference(superposition,[status(thm)],[c_27754,c_62]) ).
cnf(c_28083,plain,
least_upper_bound(multiply(X0,multiply(identity,identity)),a) = multiply(least_upper_bound(X0,a),multiply(identity,identity)),
inference(superposition,[status(thm)],[c_27754,c_64]) ).
cnf(c_28093,plain,
multiply(a,least_upper_bound(X0,multiply(identity,identity))) = least_upper_bound(a,multiply(a,X0)),
inference(theory_normalisation,[status(thm)],[c_28077,c_57,c_55,c_56,c_54]) ).
cnf(c_28094,plain,
least_upper_bound(a,multiply(a,X0)) = multiply(a,least_upper_bound(X0,identity)),
inference(light_normalisation,[status(thm)],[c_28093,c_24057]) ).
cnf(c_28099,plain,
least_upper_bound(a,multiply(X0,multiply(identity,identity))) = multiply(least_upper_bound(X0,a),multiply(identity,identity)),
inference(theory_normalisation,[status(thm)],[c_28083,c_57,c_55,c_56,c_54]) ).
cnf(c_28100,plain,
multiply(least_upper_bound(X0,a),multiply(identity,identity)) = least_upper_bound(a,X0),
inference(light_normalisation,[status(thm)],[c_28099,c_27861]) ).
cnf(c_28592,plain,
least_upper_bound(c,greatest_lower_bound(X0,c)) = least_upper_bound(c,c),
inference(superposition,[status(thm)],[c_26482,c_286]) ).
cnf(c_28622,plain,
least_upper_bound(c,c) = multiply(c,identity),
inference(light_normalisation,[status(thm)],[c_28592,c_25622]) ).
cnf(c_28809,plain,
multiply(inverse(X0),least_upper_bound(identity,X0)) = least_upper_bound(inverse(X0),identity),
inference(superposition,[status(thm)],[c_67,c_10990]) ).
cnf(c_28811,plain,
multiply(multiply(identity,identity),least_upper_bound(identity,identity)) = least_upper_bound(multiply(identity,identity),identity),
inference(superposition,[status(thm)],[c_22357,c_10990]) ).
cnf(c_28821,plain,
multiply(identity,least_upper_bound(identity,greatest_lower_bound(X0,identity))) = least_upper_bound(identity,greatest_lower_bound(identity,X0)),
inference(superposition,[status(thm)],[c_20667,c_10990]) ).
cnf(c_28822,plain,
multiply(identity,least_upper_bound(identity,least_upper_bound(X0,identity))) = least_upper_bound(identity,least_upper_bound(identity,X0)),
inference(superposition,[status(thm)],[c_23968,c_10990]) ).
cnf(c_28830,plain,
multiply(c,least_upper_bound(identity,multiply(identity,identity))) = least_upper_bound(c,c),
inference(superposition,[status(thm)],[c_27752,c_10990]) ).
cnf(c_28831,plain,
multiply(b,least_upper_bound(identity,multiply(identity,identity))) = least_upper_bound(b,b),
inference(superposition,[status(thm)],[c_27753,c_10990]) ).
cnf(c_28832,plain,
multiply(a,least_upper_bound(identity,multiply(identity,identity))) = least_upper_bound(a,a),
inference(superposition,[status(thm)],[c_27754,c_10990]) ).
cnf(c_28928,plain,
multiply(c,least_upper_bound(identity,multiply(identity,identity))) = multiply(c,identity),
inference(light_normalisation,[status(thm)],[c_28830,c_28622]) ).
cnf(c_28929,plain,
multiply(inverse(X0),least_upper_bound(identity,X0)) = least_upper_bound(identity,inverse(X0)),
inference(theory_normalisation,[status(thm)],[c_28809,c_57,c_55,c_56,c_54]) ).
cnf(c_28941,plain,
multiply(identity,least_upper_bound(identity,X0)) = least_upper_bound(X0,identity),
inference(light_normalisation,[status(thm)],[c_28822,c_11686,c_16205,c_23149]) ).
cnf(c_28942,plain,
multiply(inverse(a),a) = multiply(identity,identity),
inference(light_normalisation,[status(thm)],[c_28821,c_17532,c_17533,c_22401,c_28070]) ).
cnf(c_28943,plain,
multiply(multiply(identity,identity),least_upper_bound(identity,identity)) = least_upper_bound(identity,multiply(identity,identity)),
inference(theory_normalisation,[status(thm)],[c_28811,c_57,c_55,c_56,c_54]) ).
cnf(c_28944,plain,
least_upper_bound(identity,multiply(identity,identity)) = greatest_lower_bound(identity,multiply(identity,identity)),
inference(light_normalisation,[status(thm)],[c_28943,c_20620,c_22401]) ).
cnf(c_29447,plain,
multiply(c,greatest_lower_bound(multiply(identity,identity),identity)) = greatest_lower_bound(c,c),
inference(superposition,[status(thm)],[c_27752,c_11012]) ).
cnf(c_29448,plain,
multiply(b,greatest_lower_bound(multiply(identity,identity),identity)) = greatest_lower_bound(b,b),
inference(superposition,[status(thm)],[c_27753,c_11012]) ).
cnf(c_29449,plain,
multiply(a,greatest_lower_bound(multiply(identity,identity),identity)) = greatest_lower_bound(a,a),
inference(superposition,[status(thm)],[c_27754,c_11012]) ).
cnf(c_29525,plain,
multiply(a,greatest_lower_bound(identity,multiply(identity,identity))) = greatest_lower_bound(a,a),
inference(theory_normalisation,[status(thm)],[c_29449,c_57,c_55,c_56,c_54]) ).
cnf(c_29526,plain,
least_upper_bound(a,a) = greatest_lower_bound(a,a),
inference(light_normalisation,[status(thm)],[c_29525,c_28832,c_28944]) ).
cnf(c_29527,plain,
multiply(b,greatest_lower_bound(identity,multiply(identity,identity))) = greatest_lower_bound(b,b),
inference(theory_normalisation,[status(thm)],[c_29448,c_57,c_55,c_56,c_54]) ).
cnf(c_29528,plain,
least_upper_bound(b,b) = greatest_lower_bound(b,b),
inference(light_normalisation,[status(thm)],[c_29527,c_28831,c_28944]) ).
cnf(c_29529,plain,
multiply(c,greatest_lower_bound(identity,multiply(identity,identity))) = greatest_lower_bound(c,c),
inference(theory_normalisation,[status(thm)],[c_29447,c_57,c_55,c_56,c_54]) ).
cnf(c_29530,plain,
greatest_lower_bound(c,c) = multiply(c,identity),
inference(light_normalisation,[status(thm)],[c_29529,c_28928,c_28944]) ).
cnf(c_29591,plain,
greatest_lower_bound(least_upper_bound(a,a),X0) = greatest_lower_bound(a,greatest_lower_bound(a,X0)),
inference(superposition,[status(thm)],[c_29526,c_56]) ).
cnf(c_29631,plain,
least_upper_bound(b,least_upper_bound(b,b)) = b,
inference(superposition,[status(thm)],[c_29528,c_209]) ).
cnf(c_29696,plain,
least_upper_bound(c,multiply(c,identity)) = c,
inference(superposition,[status(thm)],[c_29530,c_209]) ).
cnf(c_31144,plain,
least_upper_bound(a,multiply(X0,identity)) = multiply(least_upper_bound(X0,a),identity),
inference(superposition,[status(thm)],[c_26872,c_64]) ).
cnf(c_31233,plain,
multiply(least_upper_bound(X0,a),identity) = least_upper_bound(a,X0),
inference(light_normalisation,[status(thm)],[c_31144,c_10954]) ).
cnf(c_31297,plain,
least_upper_bound(a,greatest_lower_bound(X0,a)) = least_upper_bound(a,a),
inference(superposition,[status(thm)],[c_26899,c_286]) ).
cnf(c_31326,plain,
least_upper_bound(a,a) = multiply(a,identity),
inference(light_normalisation,[status(thm)],[c_31297,c_25742]) ).
cnf(c_31337,plain,
greatest_lower_bound(a,a) = multiply(a,identity),
inference(demodulation,[status(thm)],[c_29526,c_31326]) ).
cnf(c_31403,plain,
greatest_lower_bound(multiply(a,identity),X0) = greatest_lower_bound(a,greatest_lower_bound(a,X0)),
inference(superposition,[status(thm)],[c_31337,c_56]) ).
cnf(c_31406,plain,
least_upper_bound(a,multiply(a,identity)) = a,
inference(superposition,[status(thm)],[c_31337,c_209]) ).
cnf(c_31451,plain,
least_upper_bound(a,least_upper_bound(X0,multiply(a,identity))) = least_upper_bound(X0,a),
inference(superposition,[status(thm)],[c_31406,c_202]) ).
cnf(c_31453,plain,
greatest_lower_bound(multiply(a,identity),greatest_lower_bound(X0,a)) = greatest_lower_bound(multiply(a,identity),X0),
inference(superposition,[status(thm)],[c_31406,c_899]) ).
cnf(c_31478,plain,
least_upper_bound(a,least_upper_bound(a,X0)) = least_upper_bound(X0,a),
inference(light_normalisation,[status(thm)],[c_31451,c_26872]) ).
cnf(c_31481,plain,
greatest_lower_bound(a,greatest_lower_bound(X0,multiply(a,identity))) = greatest_lower_bound(multiply(a,identity),X0),
inference(theory_normalisation,[status(thm)],[c_31453,c_57,c_55,c_56,c_54]) ).
cnf(c_31482,plain,
greatest_lower_bound(a,greatest_lower_bound(a,X0)) = greatest_lower_bound(X0,a),
inference(light_normalisation,[status(thm)],[c_31481,c_26900,c_31403]) ).
cnf(c_31498,plain,
least_upper_bound(least_upper_bound(X0,a),least_upper_bound(a,X0)) = multiply(least_upper_bound(X0,a),least_upper_bound(identity,identity)),
inference(superposition,[status(thm)],[c_31233,c_11011]) ).
cnf(c_31535,plain,
least_upper_bound(X0,least_upper_bound(a,least_upper_bound(a,X0))) = multiply(least_upper_bound(X0,a),least_upper_bound(identity,identity)),
inference(theory_normalisation,[status(thm)],[c_31498,c_57,c_55,c_56,c_54]) ).
cnf(c_31536,plain,
least_upper_bound(X0,least_upper_bound(X0,a)) = least_upper_bound(a,X0),
inference(light_normalisation,[status(thm)],[c_31535,c_22401,c_28100,c_31478]) ).
cnf(c_32674,plain,
least_upper_bound(b,b) = multiply(b,identity),
inference(demodulation,[status(thm)],[c_26993,c_27031]) ).
cnf(c_32678,plain,
least_upper_bound(b,multiply(b,identity)) = b,
inference(demodulation,[status(thm)],[c_29631,c_32674]) ).
cnf(c_32679,plain,
greatest_lower_bound(b,b) = multiply(b,identity),
inference(demodulation,[status(thm)],[c_29528,c_32674]) ).
cnf(c_32704,plain,
least_upper_bound(b,multiply(X0,identity)) = multiply(least_upper_bound(X0,b),identity),
inference(superposition,[status(thm)],[c_27031,c_64]) ).
cnf(c_32806,plain,
multiply(least_upper_bound(X0,b),identity) = least_upper_bound(b,X0),
inference(light_normalisation,[status(thm)],[c_32704,c_10954]) ).
cnf(c_32929,plain,
least_upper_bound(b,least_upper_bound(X0,multiply(b,identity))) = least_upper_bound(X0,b),
inference(superposition,[status(thm)],[c_32678,c_202]) ).
cnf(c_32931,plain,
greatest_lower_bound(multiply(b,identity),greatest_lower_bound(X0,b)) = greatest_lower_bound(multiply(b,identity),X0),
inference(superposition,[status(thm)],[c_32678,c_899]) ).
cnf(c_32956,plain,
least_upper_bound(b,least_upper_bound(b,X0)) = least_upper_bound(X0,b),
inference(light_normalisation,[status(thm)],[c_32929,c_27031]) ).
cnf(c_32959,plain,
greatest_lower_bound(b,greatest_lower_bound(X0,multiply(b,identity))) = greatest_lower_bound(multiply(b,identity),X0),
inference(theory_normalisation,[status(thm)],[c_32931,c_57,c_55,c_56,c_54]) ).
cnf(c_32960,plain,
greatest_lower_bound(multiply(b,identity),X0) = greatest_lower_bound(X0,b),
inference(light_normalisation,[status(thm)],[c_32959,c_27059]) ).
cnf(c_32970,plain,
greatest_lower_bound(multiply(b,identity),X0) = greatest_lower_bound(b,greatest_lower_bound(b,X0)),
inference(superposition,[status(thm)],[c_32679,c_56]) ).
cnf(c_33023,plain,
greatest_lower_bound(b,greatest_lower_bound(b,X0)) = greatest_lower_bound(X0,b),
inference(light_normalisation,[status(thm)],[c_32970,c_32960]) ).
cnf(c_33042,plain,
least_upper_bound(least_upper_bound(X0,b),least_upper_bound(b,X0)) = multiply(least_upper_bound(X0,b),least_upper_bound(identity,identity)),
inference(superposition,[status(thm)],[c_32806,c_11011]) ).
cnf(c_33079,plain,
least_upper_bound(X0,least_upper_bound(b,least_upper_bound(b,X0))) = multiply(least_upper_bound(X0,b),least_upper_bound(identity,identity)),
inference(theory_normalisation,[status(thm)],[c_33042,c_57,c_55,c_56,c_54]) ).
cnf(c_33080,plain,
least_upper_bound(X0,least_upper_bound(X0,b)) = least_upper_bound(b,X0),
inference(light_normalisation,[status(thm)],[c_33079,c_22401,c_28042,c_32956]) ).
cnf(c_35655,plain,
least_upper_bound(multiply(c,identity),identity) = multiply(identity,least_upper_bound(c,identity)),
inference(superposition,[status(thm)],[c_26427,c_28941]) ).
cnf(c_35656,plain,
least_upper_bound(multiply(a,identity),identity) = multiply(identity,least_upper_bound(a,identity)),
inference(superposition,[status(thm)],[c_26872,c_28941]) ).
cnf(c_35691,plain,
least_upper_bound(identity,multiply(a,identity)) = multiply(identity,least_upper_bound(identity,a)),
inference(theory_normalisation,[status(thm)],[c_35656,c_57,c_55,c_56,c_54]) ).
cnf(c_35692,plain,
least_upper_bound(identity,multiply(a,identity)) = multiply(identity,a),
inference(light_normalisation,[status(thm)],[c_35691,c_49]) ).
cnf(c_35693,plain,
least_upper_bound(identity,multiply(c,identity)) = multiply(identity,least_upper_bound(identity,c)),
inference(theory_normalisation,[status(thm)],[c_35655,c_57,c_55,c_56,c_54]) ).
cnf(c_35694,plain,
least_upper_bound(identity,multiply(c,identity)) = multiply(identity,c),
inference(light_normalisation,[status(thm)],[c_35693,c_51]) ).
cnf(c_36819,plain,
least_upper_bound(identity,inverse(a)) = multiply(inverse(a),a),
inference(superposition,[status(thm)],[c_49,c_28929]) ).
cnf(c_36820,plain,
least_upper_bound(identity,inverse(b)) = multiply(inverse(b),b),
inference(superposition,[status(thm)],[c_50,c_28929]) ).
cnf(c_36888,plain,
least_upper_bound(identity,inverse(a)) = multiply(identity,identity),
inference(light_normalisation,[status(thm)],[c_36819,c_28942]) ).
cnf(c_36978,plain,
greatest_lower_bound(identity,multiply(inverse(b),b)) = identity,
inference(superposition,[status(thm)],[c_36820,c_61]) ).
cnf(c_36998,plain,
multiply(multiply(inverse(b),b),b) = least_upper_bound(b,identity),
inference(superposition,[status(thm)],[c_36820,c_4098]) ).
cnf(c_36999,plain,
multiply(multiply(inverse(b),b),b) = least_upper_bound(identity,b),
inference(theory_normalisation,[status(thm)],[c_36998,c_57,c_55,c_56,c_54]) ).
cnf(c_37000,plain,
multiply(multiply(inverse(b),b),b) = b,
inference(light_normalisation,[status(thm)],[c_36999,c_50]) ).
cnf(c_37042,plain,
least_upper_bound(identity,least_upper_bound(inverse(a),X0)) = least_upper_bound(multiply(identity,identity),X0),
inference(superposition,[status(thm)],[c_36888,c_57]) ).
cnf(c_37079,plain,
least_upper_bound(identity,least_upper_bound(inverse(a),X0)) = least_upper_bound(identity,X0),
inference(light_normalisation,[status(thm)],[c_37042,c_23896]) ).
cnf(c_37290,plain,
multiply(greatest_lower_bound(identity,multiply(inverse(b),b)),b) = greatest_lower_bound(b,b),
inference(superposition,[status(thm)],[c_37000,c_457]) ).
cnf(c_37299,plain,
multiply(identity,b) = multiply(b,identity),
inference(light_normalisation,[status(thm)],[c_37290,c_32679,c_36978]) ).
cnf(c_37316,plain,
greatest_lower_bound(b,b) = multiply(identity,b),
inference(demodulation,[status(thm)],[c_32679,c_37299]) ).
cnf(c_37317,plain,
least_upper_bound(b,multiply(identity,b)) = b,
inference(demodulation,[status(thm)],[c_32678,c_37299]) ).
cnf(c_37318,plain,
least_upper_bound(b,b) = multiply(identity,b),
inference(demodulation,[status(thm)],[c_32674,c_37299]) ).
cnf(c_37551,plain,
least_upper_bound(identity,least_upper_bound(c,inverse(a))) = least_upper_bound(identity,multiply(c,identity)),
inference(superposition,[status(thm)],[c_26427,c_37079]) ).
cnf(c_37552,plain,
least_upper_bound(identity,least_upper_bound(a,inverse(a))) = least_upper_bound(identity,multiply(a,identity)),
inference(superposition,[status(thm)],[c_26872,c_37079]) ).
cnf(c_37593,plain,
least_upper_bound(a,inverse(a)) = least_upper_bound(identity,a),
inference(superposition,[status(thm)],[c_37079,c_562]) ).
cnf(c_37602,plain,
least_upper_bound(c,inverse(a)) = least_upper_bound(identity,c),
inference(superposition,[status(thm)],[c_37079,c_622]) ).
cnf(c_37626,plain,
least_upper_bound(c,inverse(a)) = c,
inference(light_normalisation,[status(thm)],[c_37602,c_51]) ).
cnf(c_37629,plain,
least_upper_bound(a,inverse(a)) = a,
inference(light_normalisation,[status(thm)],[c_37593,c_49]) ).
cnf(c_37655,plain,
least_upper_bound(identity,least_upper_bound(a,inverse(a))) = multiply(identity,a),
inference(light_normalisation,[status(thm)],[c_37552,c_35692]) ).
cnf(c_37656,plain,
least_upper_bound(identity,least_upper_bound(c,inverse(a))) = multiply(identity,c),
inference(light_normalisation,[status(thm)],[c_37551,c_35694]) ).
cnf(c_37728,plain,
least_upper_bound(c,least_upper_bound(inverse(a),X0)) = least_upper_bound(c,X0),
inference(superposition,[status(thm)],[c_37626,c_57]) ).
cnf(c_37768,plain,
least_upper_bound(a,least_upper_bound(inverse(a),X0)) = least_upper_bound(a,X0),
inference(superposition,[status(thm)],[c_37629,c_57]) ).
cnf(c_37847,plain,
greatest_lower_bound(multiply(identity,b),multiply(X0,identity)) = multiply(greatest_lower_bound(b,X0),identity),
inference(superposition,[status(thm)],[c_37299,c_65]) ).
cnf(c_37851,plain,
multiply(multiply(identity,b),X0) = multiply(b,multiply(identity,X0)),
inference(superposition,[status(thm)],[c_37299,c_68]) ).
cnf(c_37867,plain,
multiply(multiply(identity,b),X0) = multiply(b,X0),
inference(light_normalisation,[status(thm)],[c_37851,c_66]) ).
cnf(c_37876,plain,
greatest_lower_bound(multiply(identity,b),X0) = multiply(greatest_lower_bound(b,X0),identity),
inference(light_normalisation,[status(thm)],[c_37847,c_10954]) ).
cnf(c_38155,plain,
least_upper_bound(c,least_upper_bound(identity,inverse(a))) = least_upper_bound(c,multiply(identity,identity)),
inference(superposition,[status(thm)],[c_22422,c_37728]) ).
cnf(c_38272,plain,
least_upper_bound(identity,least_upper_bound(c,inverse(a))) = least_upper_bound(c,multiply(identity,identity)),
inference(theory_normalisation,[status(thm)],[c_38155,c_57,c_55,c_56,c_54]) ).
cnf(c_38273,plain,
multiply(identity,c) = multiply(c,identity),
inference(light_normalisation,[status(thm)],[c_38272,c_25625,c_37656]) ).
cnf(c_38290,plain,
least_upper_bound(c,multiply(identity,c)) = c,
inference(demodulation,[status(thm)],[c_29696,c_38273]) ).
cnf(c_38327,plain,
greatest_lower_bound(multiply(identity,b),X0) = greatest_lower_bound(b,greatest_lower_bound(b,X0)),
inference(superposition,[status(thm)],[c_37316,c_56]) ).
cnf(c_38386,plain,
multiply(greatest_lower_bound(b,X0),identity) = greatest_lower_bound(X0,b),
inference(light_normalisation,[status(thm)],[c_38327,c_33023,c_37876]) ).
cnf(c_38568,plain,
least_upper_bound(a,least_upper_bound(identity,inverse(a))) = least_upper_bound(a,multiply(identity,identity)),
inference(superposition,[status(thm)],[c_22422,c_37768]) ).
cnf(c_38659,plain,
least_upper_bound(identity,least_upper_bound(a,inverse(a))) = least_upper_bound(a,multiply(identity,identity)),
inference(theory_normalisation,[status(thm)],[c_38568,c_57,c_55,c_56,c_54]) ).
cnf(c_38660,plain,
multiply(identity,a) = multiply(a,identity),
inference(light_normalisation,[status(thm)],[c_38659,c_25745,c_37655]) ).
cnf(c_38674,plain,
least_upper_bound(a,multiply(identity,a)) = a,
inference(demodulation,[status(thm)],[c_31406,c_38660]) ).
cnf(c_38676,plain,
least_upper_bound(a,a) = multiply(identity,a),
inference(demodulation,[status(thm)],[c_31326,c_38660]) ).
cnf(c_39256,plain,
multiply(least_upper_bound(identity,identity),c) = c,
inference(superposition,[status(thm)],[c_38290,c_443]) ).
cnf(c_39263,plain,
multiply(multiply(identity,identity),c) = c,
inference(light_normalisation,[status(thm)],[c_39256,c_22401]) ).
cnf(c_39677,plain,
greatest_lower_bound(multiply(identity,a),multiply(X0,identity)) = multiply(greatest_lower_bound(a,X0),identity),
inference(superposition,[status(thm)],[c_38660,c_65]) ).
cnf(c_39681,plain,
multiply(multiply(identity,a),X0) = multiply(a,multiply(identity,X0)),
inference(superposition,[status(thm)],[c_38660,c_68]) ).
cnf(c_39697,plain,
multiply(multiply(identity,a),X0) = multiply(a,X0),
inference(light_normalisation,[status(thm)],[c_39681,c_66]) ).
cnf(c_39706,plain,
greatest_lower_bound(multiply(identity,a),X0) = multiply(greatest_lower_bound(a,X0),identity),
inference(light_normalisation,[status(thm)],[c_39677,c_10954]) ).
cnf(c_39813,plain,
multiply(greatest_lower_bound(a,X0),identity) = greatest_lower_bound(X0,a),
inference(light_normalisation,[status(thm)],[c_29591,c_31482,c_38676,c_39706]) ).
cnf(c_43472,plain,
least_upper_bound(least_upper_bound(a,a),a) = multiply(least_upper_bound(a,a),identity),
inference(superposition,[status(thm)],[c_31536,c_24934]) ).
cnf(c_43586,plain,
least_upper_bound(a,least_upper_bound(a,a)) = multiply(least_upper_bound(a,a),identity),
inference(theory_normalisation,[status(thm)],[c_43472,c_57,c_55,c_56,c_54]) ).
cnf(c_43587,plain,
multiply(multiply(identity,a),identity) = a,
inference(light_normalisation,[status(thm)],[c_43586,c_38674,c_38676]) ).
cnf(c_43610,plain,
least_upper_bound(a,multiply(multiply(identity,a),X0)) = multiply(multiply(identity,a),least_upper_bound(identity,X0)),
inference(superposition,[status(thm)],[c_43587,c_62]) ).
cnf(c_43647,plain,
multiply(multiply(identity,a),least_upper_bound(identity,X0)) = multiply(a,least_upper_bound(X0,identity)),
inference(light_normalisation,[status(thm)],[c_43610,c_28094,c_39697]) ).
cnf(c_43654,plain,
greatest_lower_bound(multiply(identity,b),X0) = greatest_lower_bound(X0,b),
inference(light_normalisation,[status(thm)],[c_37876,c_38386]) ).
cnf(c_43686,plain,
greatest_lower_bound(X0,multiply(identity,b)) = greatest_lower_bound(X0,b),
inference(superposition,[status(thm)],[c_43654,c_54]) ).
cnf(c_44268,plain,
greatest_lower_bound(multiply(identity,b),a) = multiply(greatest_lower_bound(a,b),identity),
inference(superposition,[status(thm)],[c_43686,c_39813]) ).
cnf(c_44339,plain,
greatest_lower_bound(a,multiply(identity,b)) = multiply(greatest_lower_bound(a,b),identity),
inference(theory_normalisation,[status(thm)],[c_44268,c_57,c_55,c_56,c_54]) ).
cnf(c_44340,plain,
greatest_lower_bound(a,multiply(identity,b)) = multiply(identity,identity),
inference(light_normalisation,[status(thm)],[c_44339,c_52]) ).
cnf(c_46823,plain,
least_upper_bound(least_upper_bound(b,b),b) = multiply(least_upper_bound(b,b),identity),
inference(superposition,[status(thm)],[c_33080,c_24938]) ).
cnf(c_46941,plain,
least_upper_bound(b,least_upper_bound(b,b)) = multiply(least_upper_bound(b,b),identity),
inference(theory_normalisation,[status(thm)],[c_46823,c_57,c_55,c_56,c_54]) ).
cnf(c_46942,plain,
multiply(multiply(identity,b),identity) = b,
inference(light_normalisation,[status(thm)],[c_46941,c_37317,c_37318]) ).
cnf(c_46967,plain,
least_upper_bound(b,multiply(multiply(identity,b),X0)) = multiply(multiply(identity,b),least_upper_bound(identity,X0)),
inference(superposition,[status(thm)],[c_46942,c_62]) ).
cnf(c_47004,plain,
multiply(multiply(identity,b),least_upper_bound(identity,X0)) = multiply(b,least_upper_bound(X0,identity)),
inference(light_normalisation,[status(thm)],[c_46967,c_28036,c_37867]) ).
cnf(c_47298,plain,
greatest_lower_bound(multiply(identity,a),X0) = greatest_lower_bound(X0,a),
inference(light_normalisation,[status(thm)],[c_39706,c_39813]) ).
cnf(c_608247,plain,
multiply(multiply(identity,a),c) = multiply(a,least_upper_bound(c,identity)),
inference(superposition,[status(thm)],[c_51,c_43647]) ).
cnf(c_608613,plain,
multiply(multiply(identity,a),c) = multiply(a,least_upper_bound(identity,c)),
inference(theory_normalisation,[status(thm)],[c_608247,c_57,c_55,c_56,c_54]) ).
cnf(c_608614,plain,
multiply(multiply(identity,a),c) = multiply(a,c),
inference(light_normalisation,[status(thm)],[c_608613,c_51]) ).
cnf(c_609357,plain,
greatest_lower_bound(multiply(identity,a),multiply(a,c)) = multiply(multiply(identity,a),greatest_lower_bound(identity,c)),
inference(superposition,[status(thm)],[c_608614,c_10989]) ).
cnf(c_609381,plain,
greatest_lower_bound(multiply(identity,a),multiply(a,c)) = a,
inference(light_normalisation,[status(thm)],[c_609357,c_215,c_43587]) ).
cnf(c_609563,plain,
greatest_lower_bound(multiply(a,c),a) = a,
inference(superposition,[status(thm)],[c_609381,c_47298]) ).
cnf(c_609567,plain,
greatest_lower_bound(a,multiply(a,c)) = a,
inference(theory_normalisation,[status(thm)],[c_609563,c_57,c_55,c_56,c_54]) ).
cnf(c_609674,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(a,c),X0)) = greatest_lower_bound(a,X0),
inference(superposition,[status(thm)],[c_609567,c_56]) ).
cnf(c_609948,plain,
greatest_lower_bound(a,multiply(greatest_lower_bound(a,X0),c)) = greatest_lower_bound(a,multiply(X0,c)),
inference(superposition,[status(thm)],[c_65,c_609674]) ).
cnf(c_657645,plain,
multiply(multiply(identity,b),c) = multiply(b,least_upper_bound(c,identity)),
inference(superposition,[status(thm)],[c_51,c_47004]) ).
cnf(c_658022,plain,
multiply(multiply(identity,b),c) = multiply(b,least_upper_bound(identity,c)),
inference(theory_normalisation,[status(thm)],[c_657645,c_57,c_55,c_56,c_54]) ).
cnf(c_658023,plain,
multiply(multiply(identity,b),c) = multiply(b,c),
inference(light_normalisation,[status(thm)],[c_658022,c_51]) ).
cnf(c_1218817,plain,
greatest_lower_bound(a,multiply(multiply(identity,identity),c)) = greatest_lower_bound(a,multiply(multiply(identity,b),c)),
inference(superposition,[status(thm)],[c_44340,c_609948]) ).
cnf(c_1219058,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c),
inference(light_normalisation,[status(thm)],[c_1218817,c_39263,c_658023]) ).
cnf(c_1219059,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1219058,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : GRP178-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.09/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 2 23:46:58 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running UEQ theorem proving
% 0.18/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule casc_24_ueq --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 295.66/38.19 % SZS status Started for theBenchmark.p
% 295.66/38.19 % SZS status Unsatisfiable for theBenchmark.p
% 295.66/38.19
% 295.66/38.19 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 295.66/38.19
% 295.66/38.19 ------ iProver source info
% 295.66/38.19
% 295.66/38.19 git: date: 2024-05-02 19:28:25 +0000
% 295.66/38.19 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 295.66/38.19 git: non_committed_changes: false
% 295.66/38.19
% 295.66/38.19 ------ Parsing...successful
% 295.66/38.19
% 295.66/38.19
% 295.66/38.19
% 295.66/38.19 ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e
% 295.66/38.19
% 295.66/38.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 295.66/38.19
% 295.66/38.19 ------ Preprocessing... sf_s rm: 0 0s sf_e
% 295.66/38.19 ------ Proving...
% 295.66/38.19 ------ Problem Properties
% 295.66/38.19
% 295.66/38.19
% 295.66/38.19 clauses 20
% 295.66/38.19 conjectures 1
% 295.66/38.19 EPR 0
% 295.66/38.19 Horn 20
% 295.66/38.19 unary 20
% 295.66/38.19 binary 0
% 295.66/38.19 lits 20
% 295.66/38.19 lits eq 20
% 295.66/38.19 fd_pure 0
% 295.66/38.19 fd_pseudo 0
% 295.66/38.19 fd_cond 0
% 295.66/38.19 fd_pseudo_cond 0
% 295.66/38.19 AC symbols 2
% 295.66/38.19
% 295.66/38.19 ------ Input Options Time Limit: Unbounded
% 295.66/38.19
% 295.66/38.19
% 295.66/38.19 ------
% 295.66/38.19 Current options:
% 295.66/38.19 ------
% 295.66/38.19
% 295.66/38.19
% 295.66/38.19
% 295.66/38.19
% 295.66/38.19 ------ Proving...
% 295.66/38.19
% 295.66/38.19
% 295.66/38.19 % SZS status Unsatisfiable for theBenchmark.p
% 295.66/38.19
% 295.66/38.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 295.66/38.19
% 295.66/38.20
%------------------------------------------------------------------------------