TSTP Solution File: GRP184-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP184-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 00:17:35 EDT 2023
% Result : Unsatisfiable 3.34s 3.47s
% Output : CNFRefutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 24
% Syntax : Number of formulae : 142 ( 136 unt; 6 typ; 0 def)
% Number of atoms : 136 ( 135 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 5 ( 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 250 ( 22 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 ).
cnf(p21_3,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_3) ).
cnf(p21_1,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_1) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(p21_2,hypothesis,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21_2) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
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/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
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/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
cnf(prove_p21,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p21) ).
cnf(c_0_18,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
p21_3 ).
cnf(c_0_19,hypothesis,
inverse(identity) = identity,
p21_1 ).
cnf(c_0_20,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_21,hypothesis,
multiply(inverse(X1),identity) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_22,hypothesis,
inverse(inverse(X1)) = X1,
p21_2 ).
cnf(c_0_23,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_24,hypothesis,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_26,hypothesis,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_27,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_28,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_29,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_30,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_31,hypothesis,
multiply(inverse(X1),greatest_lower_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_25]) ).
cnf(c_0_32,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_34,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_35,hypothesis,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_36,hypothesis,
multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_37,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_32,c_0_33]),c_0_25]) ).
cnf(c_0_38,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_39,hypothesis,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_40,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_41,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_42,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_34,c_0_20]),c_0_25]) ).
cnf(c_0_43,hypothesis,
multiply(inverse(greatest_lower_bound(X1,identity)),X1) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_44,hypothesis,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_27]) ).
cnf(c_0_45,hypothesis,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_20]) ).
cnf(c_0_46,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_47,hypothesis,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_24]),c_0_29]) ).
cnf(c_0_48,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_41,c_0_20]),c_0_29]) ).
cnf(c_0_49,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_27]),c_0_20]) ).
cnf(c_0_50,hypothesis,
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_42,c_0_43]),c_0_25]),c_0_44]),c_0_20]) ).
cnf(c_0_51,hypothesis,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_45]),c_0_22]) ).
cnf(c_0_52,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_46,c_0_28]) ).
cnf(c_0_53,hypothesis,
multiply(least_upper_bound(X1,identity),X1) = multiply(X1,least_upper_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
multiply(inverse(X1),least_upper_bound(multiply(X1,X2),X3)) = least_upper_bound(X2,multiply(inverse(X1),X3)),
inference(spm,[status(thm)],[c_0_40,c_0_49]) ).
cnf(c_0_55,hypothesis,
least_upper_bound(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_50]),c_0_29]) ).
cnf(c_0_56,hypothesis,
multiply(greatest_lower_bound(X1,inverse(multiply(X2,X3))),X2) = greatest_lower_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_34,c_0_51]) ).
cnf(c_0_57,hypothesis,
greatest_lower_bound(X1,multiply(least_upper_bound(X1,X2),greatest_lower_bound(X3,identity))) = greatest_lower_bound(X1,multiply(least_upper_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_52,c_0_26]) ).
cnf(c_0_58,hypothesis,
multiply(least_upper_bound(X1,identity),greatest_lower_bound(X1,identity)) = multiply(greatest_lower_bound(X1,identity),least_upper_bound(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_53]),c_0_42]) ).
cnf(c_0_59,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_60,plain,
multiply(least_upper_bound(inverse(X1),X2),X1) = least_upper_bound(identity,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_61,hypothesis,
least_upper_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = inverse(greatest_lower_bound(X2,inverse(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_54,c_0_55]),c_0_18]),c_0_56]),c_0_20]),c_0_18]),c_0_56]),c_0_20]) ).
cnf(c_0_62,hypothesis,
greatest_lower_bound(X1,multiply(greatest_lower_bound(X1,identity),least_upper_bound(X1,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_57,c_0_58]),c_0_53]),c_0_26]),c_0_25]),c_0_32]),c_0_24]) ).
cnf(c_0_63,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_59,c_0_30]) ).
cnf(c_0_64,hypothesis,
multiply(least_upper_bound(X1,inverse(multiply(X2,X3))),X2) = least_upper_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_41,c_0_51]) ).
cnf(c_0_65,plain,
multiply(least_upper_bound(X1,inverse(X2)),X2) = least_upper_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_27]),c_0_29]) ).
cnf(c_0_66,hypothesis,
least_upper_bound(identity,multiply(inverse(greatest_lower_bound(X1,X2)),X2)) = multiply(inverse(greatest_lower_bound(X1,X2)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_22]),c_0_22]) ).
cnf(c_0_67,hypothesis,
greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),least_upper_bound(X1,identity))) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_25]) ).
cnf(c_0_68,hypothesis,
multiply(inverse(X1),multiply(greatest_lower_bound(identity,X1),X2)) = multiply(greatest_lower_bound(identity,inverse(X1)),X2),
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_69,hypothesis,
least_upper_bound(X1,multiply(greatest_lower_bound(X1,X2),least_upper_bound(X3,identity))) = least_upper_bound(X1,multiply(greatest_lower_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_63,c_0_47]) ).
cnf(c_0_70,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_34,c_0_27]),c_0_25]) ).
cnf(c_0_71,hypothesis,
multiply(least_upper_bound(X1,multiply(X2,X3)),inverse(X3)) = least_upper_bound(multiply(X1,inverse(X3)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_18]),c_0_22]),c_0_22]) ).
cnf(c_0_72,hypothesis,
multiply(least_upper_bound(X1,identity),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_39]),c_0_29]) ).
cnf(c_0_73,plain,
multiply(least_upper_bound(X1,least_upper_bound(X2,inverse(X3))),X3) = least_upper_bound(identity,multiply(least_upper_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_65,c_0_59]) ).
cnf(c_0_74,hypothesis,
multiply(X1,least_upper_bound(X2,multiply(inverse(X1),X3))) = least_upper_bound(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_40,c_0_45]) ).
cnf(c_0_75,hypothesis,
multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(X1,identity)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_69]),c_0_70]),c_0_20]),c_0_30]),c_0_68]) ).
cnf(c_0_76,hypothesis,
least_upper_bound(X1,least_upper_bound(identity,multiply(X2,X1))) = least_upper_bound(identity,multiply(least_upper_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_71,c_0_72]),c_0_22]),c_0_73]),c_0_22]),c_0_29]),c_0_59]) ).
cnf(c_0_77,hypothesis,
least_upper_bound(X1,least_upper_bound(X2,multiply(least_upper_bound(X1,X2),X3))) = multiply(least_upper_bound(X1,X2),least_upper_bound(X3,identity)),
inference(spm,[status(thm)],[c_0_59,c_0_47]) ).
cnf(c_0_78,axiom,
least_upper_bound(X1,X1) = X1,
idempotence_of_lub ).
cnf(c_0_79,hypothesis,
multiply(inverse(least_upper_bound(multiply(X1,X2),X3)),X1) = inverse(least_upper_bound(X2,multiply(inverse(X1),X3))),
inference(spm,[status(thm)],[c_0_51,c_0_74]) ).
cnf(c_0_80,hypothesis,
inverse(least_upper_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_75]),c_0_19]),c_0_20]) ).
cnf(c_0_81,hypothesis,
least_upper_bound(identity,multiply(X1,least_upper_bound(X1,identity))) = multiply(least_upper_bound(X1,identity),least_upper_bound(X1,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_59]),c_0_78]),c_0_53]) ).
cnf(c_0_82,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_33,c_0_32]),c_0_29]) ).
cnf(c_0_83,hypothesis,
inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_56]),c_0_20]),c_0_24]) ).
cnf(c_0_84,plain,
greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_59]) ).
cnf(c_0_85,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_33,c_0_46]) ).
cnf(c_0_86,hypothesis,
least_upper_bound(X1,inverse(least_upper_bound(X1,identity))) = 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(spm,[status(thm)],[c_0_71,c_0_81]),c_0_38]),c_0_39]),c_0_24]),c_0_20]),c_0_29]) ).
cnf(c_0_87,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_59,c_0_33]) ).
cnf(c_0_88,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_59,c_0_82]),c_0_59]),c_0_59]) ).
cnf(c_0_89,hypothesis,
inverse(greatest_lower_bound(X1,inverse(X2))) = least_upper_bound(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_83]) ).
cnf(c_0_90,hypothesis,
multiply(greatest_lower_bound(X1,identity),X1) = multiply(X1,greatest_lower_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_26,c_0_42]) ).
cnf(c_0_91,hypothesis,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_72,c_0_29]) ).
cnf(c_0_92,plain,
greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_84,c_0_29]) ).
cnf(c_0_93,hypothesis,
least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_44]),c_0_29]) ).
cnf(c_0_94,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_85,c_0_28]),c_0_59]) ).
cnf(c_0_95,hypothesis,
least_upper_bound(X1,greatest_lower_bound(identity,inverse(X1))) = least_upper_bound(X1,identity),
inference(rw,[status(thm)],[c_0_86,c_0_80]) ).
cnf(c_0_96,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_87,c_0_28]),c_0_59]),c_0_59]),c_0_88]) ).
cnf(c_0_97,hypothesis,
least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_89,c_0_19]) ).
cnf(c_0_98,hypothesis,
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_46,c_0_26]) ).
cnf(c_0_99,hypothesis,
multiply(greatest_lower_bound(identity,X1),X1) = multiply(X1,greatest_lower_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_90,c_0_25]) ).
cnf(c_0_100,hypothesis,
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_56,c_0_18]),c_0_22]),c_0_22]) ).
cnf(c_0_101,hypothesis,
multiply(greatest_lower_bound(X1,identity),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_39]),c_0_25]) ).
cnf(c_0_102,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_70,c_0_46]) ).
cnf(c_0_103,hypothesis,
multiply(inverse(least_upper_bound(identity,inverse(X1))),least_upper_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_91]),c_0_22]) ).
cnf(c_0_104,hypothesis,
inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_80,c_0_29]) ).
cnf(c_0_105,hypothesis,
greatest_lower_bound(identity,least_upper_bound(X1,inverse(greatest_lower_bound(X2,identity)))) = identity,
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_106,hypothesis,
least_upper_bound(X1,inverse(greatest_lower_bound(X1,identity))) = least_upper_bound(X1,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]),c_0_29]),c_0_97]),c_0_29]) ).
cnf(c_0_107,hypothesis,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_108,hypothesis,
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_40,c_0_39]),c_0_29]) ).
cnf(c_0_109,hypothesis,
greatest_lower_bound(identity,multiply(X1,greatest_lower_bound(X1,identity))) = multiply(greatest_lower_bound(identity,X1),greatest_lower_bound(X1,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_26]),c_0_46]),c_0_37]) ).
cnf(c_0_110,hypothesis,
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_100,c_0_101]),c_0_22]),c_0_102]),c_0_22]),c_0_25]),c_0_46]) ).
cnf(c_0_111,hypothesis,
multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_104]),c_0_22]) ).
cnf(c_0_112,plain,
greatest_lower_bound(X1,multiply(greatest_lower_bound(X2,identity),least_upper_bound(X1,X3))) = greatest_lower_bound(X1,multiply(X2,least_upper_bound(X1,X3))),
inference(spm,[status(thm)],[c_0_52,c_0_42]) ).
cnf(c_0_113,hypothesis,
greatest_lower_bound(identity,multiply(X1,inverse(X2))) = multiply(greatest_lower_bound(X1,X2),inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_39]),c_0_25]) ).
cnf(c_0_114,hypothesis,
greatest_lower_bound(identity,least_upper_bound(X1,inverse(X1))) = identity,
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_115,hypothesis,
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_107,c_0_100]) ).
cnf(c_0_116,plain,
greatest_lower_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),greatest_lower_bound(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_117,hypothesis,
greatest_lower_bound(least_upper_bound(X1,inverse(X2)),least_upper_bound(identity,multiply(X2,X1))) = multiply(greatest_lower_bound(X2,identity),least_upper_bound(X1,inverse(X2))),
inference(spm,[status(thm)],[c_0_42,c_0_108]) ).
cnf(c_0_118,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_85,c_0_25]) ).
cnf(c_0_119,hypothesis,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X1,identity))) = 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(spm,[status(thm)],[c_0_100,c_0_109]),c_0_38]),c_0_39]),c_0_24]),c_0_20]),c_0_25]) ).
cnf(c_0_120,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
prove_p21 ).
cnf(c_0_121,hypothesis,
greatest_lower_bound(identity,multiply(X1,least_upper_bound(identity,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_110,c_0_111]),c_0_25]),c_0_46]),c_0_32]),c_0_46]),c_0_37]),c_0_112]) ).
cnf(c_0_122,hypothesis,
greatest_lower_bound(identity,greatest_lower_bound(X1,inverse(X1))) = greatest_lower_bound(X1,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_83]),c_0_20]),c_0_83]),c_0_20]) ).
cnf(c_0_123,hypothesis,
multiply(X1,multiply(inverse(greatest_lower_bound(X2,X1)),X2)) = inverse(greatest_lower_bound(inverse(X1),inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_35]),c_0_20]) ).
cnf(c_0_124,hypothesis,
greatest_lower_bound(least_upper_bound(identity,X1),inverse(greatest_lower_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_97]),c_0_24]),c_0_39]),c_0_25]) ).
cnf(c_0_125,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_118,c_0_52]),c_0_59]) ).
cnf(c_0_126,hypothesis,
least_upper_bound(inverse(X1),greatest_lower_bound(X1,identity)) = inverse(greatest_lower_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_119]),c_0_29]) ).
cnf(c_0_127,negated_conjecture,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != multiply(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_25]),c_0_29]),c_0_29]),c_0_25]) ).
cnf(c_0_128,hypothesis,
multiply(least_upper_bound(identity,X1),inverse(greatest_lower_bound(identity,X1))) = least_upper_bound(X1,inverse(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_115,c_0_121]),c_0_20]),c_0_104]),c_0_46]),c_0_25]),c_0_122]),c_0_89]) ).
cnf(c_0_129,hypothesis,
multiply(X1,multiply(inverse(greatest_lower_bound(X2,X1)),X2)) = least_upper_bound(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_89]),c_0_22]) ).
cnf(c_0_130,hypothesis,
greatest_lower_bound(least_upper_bound(identity,X1),inverse(greatest_lower_bound(identity,X1))) = identity,
inference(spm,[status(thm)],[c_0_124,c_0_25]) ).
cnf(c_0_131,hypothesis,
least_upper_bound(X1,inverse(greatest_lower_bound(identity,X1))) = least_upper_bound(X1,inverse(X1)),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_132,hypothesis,
least_upper_bound(identity,least_upper_bound(X1,inverse(X2))) = least_upper_bound(X1,inverse(greatest_lower_bound(X2,identity))),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_133,negated_conjecture,
multiply(inverse(greatest_lower_bound(identity,a)),least_upper_bound(identity,a)) != least_upper_bound(a,inverse(a)),
inference(rw,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_134,hypothesis,
multiply(inverse(greatest_lower_bound(identity,X1)),least_upper_bound(identity,X1)) = least_upper_bound(X1,inverse(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_129,c_0_130]),c_0_19]),c_0_20]),c_0_59]),c_0_131]),c_0_132]),c_0_106]) ).
cnf(c_0_135,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : GRP184-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Mon Aug 28 20:40:15 EDT 2023
% 0.11/0.30 % CPUTime :
% 0.15/0.48 start to proof: theBenchmark
% 3.34/3.47 % Version : CSE_E---1.5
% 3.34/3.47 % Problem : theBenchmark.p
% 3.34/3.47 % Proof found
% 3.34/3.47 % SZS status Theorem for theBenchmark.p
% 3.34/3.47 % SZS output start Proof
% See solution above
% 3.34/3.48 % Total time : 2.978000 s
% 3.34/3.48 % SZS output end Proof
% 3.34/3.48 % Total time : 2.981000 s
%------------------------------------------------------------------------------