TSTP Solution File: GRP167-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP167-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 00:17:23 EDT 2023
% Result : Unsatisfiable 1.10s 1.18s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 25
% Syntax : Number of formulae : 108 ( 100 unt; 8 typ; 0 def)
% Number of atoms : 100 ( 99 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 179 ( 13 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,
positive_part: $i > $i ).
tff(decl_28,type,
negative_part: $i > $i ).
tff(decl_29,type,
a: $i ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
cnf(lat4_4,axiom,
greatest_lower_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_4) ).
cnf(prove_lat4,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat4) ).
cnf(lat4_1,axiom,
positive_part(X1) = least_upper_bound(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_1) ).
cnf(lat4_2,axiom,
negative_part(X1) = greatest_lower_bound(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_2) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(c_0_17,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_18,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_19,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_20,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_21,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_22,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_20]) ).
cnf(c_0_23,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_23]) ).
cnf(c_0_25,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_26,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_27,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_28,plain,
multiply(X1,least_upper_bound(X2,inverse(X1))) = least_upper_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_29,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_30,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_31,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_32,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_33,plain,
multiply(X1,multiply(least_upper_bound(X2,inverse(X1)),X3)) = multiply(least_upper_bound(identity,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_17,c_0_28]) ).
cnf(c_0_34,plain,
multiply(least_upper_bound(X1,X2),inverse(X2)) = least_upper_bound(identity,multiply(X1,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_27]) ).
cnf(c_0_35,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_23]),c_0_31]) ).
cnf(c_0_36,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_37,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_38,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_32,c_0_19]),c_0_31]) ).
cnf(c_0_39,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_40,plain,
multiply(least_upper_bound(identity,multiply(X1,X2)),X1) = multiply(X1,least_upper_bound(identity,multiply(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_24]),c_0_24]) ).
cnf(c_0_41,plain,
multiply(inverse(X1),greatest_lower_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_18]),c_0_31]) ).
cnf(c_0_42,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_43,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_27]) ).
cnf(c_0_44,plain,
greatest_lower_bound(X1,multiply(X2,multiply(X3,X1))) = multiply(greatest_lower_bound(identity,multiply(X2,X3)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_17]),c_0_31]) ).
cnf(c_0_45,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_39]),c_0_23]) ).
cnf(c_0_46,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_23]),c_0_19]) ).
cnf(c_0_47,plain,
multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_41,c_0_31]) ).
cnf(c_0_48,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_49,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_42,c_0_43]),c_0_27]) ).
cnf(c_0_50,plain,
least_upper_bound(X1,least_upper_bound(X1,X2)) = least_upper_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_37]),c_0_27]) ).
cnf(c_0_51,plain,
multiply(greatest_lower_bound(identity,multiply(X1,X2)),X1) = multiply(X1,greatest_lower_bound(identity,multiply(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_44]),c_0_31]) ).
cnf(c_0_52,plain,
multiply(X1,inverse(multiply(X1,least_upper_bound(identity,X1)))) = inverse(least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_37]),c_0_23]) ).
cnf(c_0_54,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_45]),c_0_24]) ).
cnf(c_0_55,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_56,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_48,c_0_42]) ).
cnf(c_0_57,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_48,c_0_49]),c_0_48]),c_0_48]) ).
cnf(c_0_58,plain,
multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_59,plain,
least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_50]),c_0_26]) ).
cnf(c_0_60,plain,
least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X2,X1)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_49]),c_0_26]) ).
cnf(c_0_61,plain,
multiply(X1,least_upper_bound(X2,inverse(multiply(X3,X1)))) = least_upper_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_62,plain,
multiply(inverse(least_upper_bound(identity,X1)),X1) = multiply(X1,inverse(least_upper_bound(identity,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54]),c_0_53]) ).
cnf(c_0_63,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_55,c_0_45]) ).
cnf(c_0_64,plain,
multiply(X1,least_upper_bound(X2,least_upper_bound(X3,inverse(X1)))) = least_upper_bound(identity,multiply(X1,least_upper_bound(X2,X3))),
inference(spm,[status(thm)],[c_0_28,c_0_48]) ).
cnf(c_0_65,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_56,c_0_37]),c_0_48]),c_0_48]),c_0_57]) ).
cnf(c_0_66,plain,
multiply(greatest_lower_bound(X1,identity),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_26]),c_0_31]) ).
cnf(c_0_67,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_68,plain,
least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_23]),c_0_23]) ).
cnf(c_0_69,plain,
least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_60]),c_0_23]),c_0_23]) ).
cnf(c_0_70,plain,
least_upper_bound(identity,least_upper_bound(X1,multiply(X1,X2))) = least_upper_bound(identity,multiply(X1,least_upper_bound(X2,identity))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]),c_0_34]),c_0_19]),c_0_64]),c_0_24]),c_0_65]),c_0_27]) ).
cnf(c_0_71,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_66,c_0_31]) ).
cnf(c_0_72,axiom,
greatest_lower_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,X3)),
lat4_4 ).
cnf(c_0_73,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_67]) ).
cnf(c_0_74,plain,
least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_24]) ).
cnf(c_0_75,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
prove_lat4 ).
cnf(c_0_76,axiom,
positive_part(X1) = least_upper_bound(X1,identity),
lat4_1 ).
cnf(c_0_77,axiom,
negative_part(X1) = greatest_lower_bound(X1,identity),
lat4_2 ).
cnf(c_0_78,plain,
least_upper_bound(inverse(X1),multiply(inverse(X1),X2)) = multiply(inverse(X1),least_upper_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_26]),c_0_27]) ).
cnf(c_0_79,plain,
multiply(inverse(least_upper_bound(X1,identity)),X1) = multiply(X1,inverse(least_upper_bound(X1,identity))),
inference(spm,[status(thm)],[c_0_62,c_0_27]) ).
cnf(c_0_80,plain,
least_upper_bound(inverse(X1),multiply(X2,inverse(X1))) = multiply(least_upper_bound(identity,X2),inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_20]),c_0_17]),c_0_58]),c_0_23]) ).
cnf(c_0_81,plain,
greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(least_upper_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_69]),c_0_31]) ).
cnf(c_0_82,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,inverse(X1)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_36]),c_0_27]) ).
cnf(c_0_83,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_18,c_0_73]) ).
cnf(c_0_84,plain,
least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_74,c_0_49]) ).
cnf(c_0_85,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_86,plain,
multiply(greatest_lower_bound(identity,X1),inverse(greatest_lower_bound(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_47]),c_0_24]) ).
cnf(c_0_87,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X1))),greatest_lower_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_71]),c_0_24]) ).
cnf(c_0_88,plain,
multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_18]) ).
cnf(c_0_89,plain,
multiply(greatest_lower_bound(X1,inverse(multiply(X2,X3))),X2) = greatest_lower_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_32,c_0_54]) ).
cnf(c_0_90,plain,
greatest_lower_bound(identity,inverse(multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,inverse(X1))))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_83]),c_0_31]) ).
cnf(c_0_91,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_92,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = inverse(least_upper_bound(X2,inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_84]),c_0_31]) ).
cnf(c_0_93,negated_conjecture,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_31]),c_0_27]) ).
cnf(c_0_94,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_86]),c_0_87]) ).
cnf(c_0_95,plain,
multiply(least_upper_bound(identity,X1),inverse(least_upper_bound(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_88]),c_0_23]),c_0_23]),c_0_27]) ).
cnf(c_0_96,plain,
inverse(least_upper_bound(identity,inverse(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(spm,[status(thm)],[c_0_89,c_0_90]),c_0_19]),c_0_19]),c_0_91]),c_0_92]),c_0_53]) ).
cnf(c_0_97,negated_conjecture,
multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)) != a,
inference(rw,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_98,plain,
multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96]),c_0_94]) ).
cnf(c_0_99,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP167-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 21:04:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 1.10/1.18 % Version : CSE_E---1.5
% 1.10/1.18 % Problem : theBenchmark.p
% 1.10/1.18 % Proof found
% 1.10/1.18 % SZS status Theorem for theBenchmark.p
% 1.10/1.18 % SZS output start Proof
% See solution above
% 1.10/1.18 % Total time : 0.596000 s
% 1.10/1.18 % SZS output end Proof
% 1.10/1.18 % Total time : 0.599000 s
%------------------------------------------------------------------------------