TSTP Solution File: GRP183-4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP183-4 : 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 : n013.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 2.14s 2.18s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 89 ( 83 unt; 6 typ; 0 def)
% Number of atoms : 83 ( 82 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 : 150 ( 9 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(p20x_3,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20x_3) ).
cnf(p20x_1,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20x_1) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(p20x_2,hypothesis,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20x_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(prove_20x,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_20x) ).
cnf(c_0_17,hypothesis,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
p20x_3 ).
cnf(c_0_18,hypothesis,
inverse(identity) = identity,
p20x_1 ).
cnf(c_0_19,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_20,hypothesis,
multiply(inverse(X1),identity) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_21,hypothesis,
inverse(inverse(X1)) = X1,
p20x_2 ).
cnf(c_0_22,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_23,hypothesis,
multiply(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_25,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_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_27,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_28,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_29,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_30,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_25,c_0_26]),c_0_24]) ).
cnf(c_0_31,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_33,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_34,hypothesis,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_35,hypothesis,
multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_36,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_31,c_0_32]),c_0_24]) ).
cnf(c_0_37,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_38,hypothesis,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_39,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_40,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_41,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_33,c_0_19]),c_0_24]) ).
cnf(c_0_42,hypothesis,
multiply(inverse(greatest_lower_bound(X1,identity)),X1) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_43,hypothesis,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_26]) ).
cnf(c_0_44,hypothesis,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_19]) ).
cnf(c_0_45,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_46,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_39,c_0_23]),c_0_28]) ).
cnf(c_0_47,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_40,c_0_19]),c_0_28]) ).
cnf(c_0_48,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_26]),c_0_19]) ).
cnf(c_0_49,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_41,c_0_42]),c_0_24]),c_0_43]),c_0_19]) ).
cnf(c_0_50,hypothesis,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_44]),c_0_21]) ).
cnf(c_0_51,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_45,c_0_27]) ).
cnf(c_0_52,hypothesis,
multiply(least_upper_bound(X1,identity),X1) = multiply(X1,least_upper_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,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_39,c_0_48]) ).
cnf(c_0_54,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_32,c_0_49]),c_0_28]) ).
cnf(c_0_55,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_33,c_0_50]) ).
cnf(c_0_56,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_51,c_0_25]) ).
cnf(c_0_57,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_25,c_0_52]),c_0_41]) ).
cnf(c_0_58,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_59,plain,
multiply(least_upper_bound(inverse(X1),X2),X1) = least_upper_bound(identity,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_26]) ).
cnf(c_0_60,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_53,c_0_54]),c_0_17]),c_0_55]),c_0_19]),c_0_17]),c_0_55]),c_0_19]) ).
cnf(c_0_61,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_56,c_0_57]),c_0_52]),c_0_25]),c_0_24]),c_0_31]),c_0_23]) ).
cnf(c_0_62,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_58,c_0_29]) ).
cnf(c_0_63,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_59,c_0_60]),c_0_21]),c_0_21]) ).
cnf(c_0_64,hypothesis,
greatest_lower_bound(X1,multiply(greatest_lower_bound(identity,X1),least_upper_bound(X1,identity))) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_24]) ).
cnf(c_0_65,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_37,c_0_35]) ).
cnf(c_0_66,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_62,c_0_46]) ).
cnf(c_0_67,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_33,c_0_26]),c_0_24]) ).
cnf(c_0_68,hypothesis,
multiply(X1,least_upper_bound(X2,multiply(inverse(X1),X3))) = least_upper_bound(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_39,c_0_44]) ).
cnf(c_0_69,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_63,c_0_64]),c_0_65]),c_0_66]),c_0_67]),c_0_19]),c_0_29]),c_0_65]) ).
cnf(c_0_70,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_50,c_0_68]) ).
cnf(c_0_71,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_50,c_0_69]),c_0_18]),c_0_19]) ).
cnf(c_0_72,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_70,c_0_71]),c_0_55]),c_0_19]),c_0_23]) ).
cnf(c_0_73,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_39,c_0_38]),c_0_28]) ).
cnf(c_0_74,hypothesis,
inverse(greatest_lower_bound(X1,inverse(X2))) = least_upper_bound(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_21,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
prove_20x ).
cnf(c_0_76,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_41,c_0_73]) ).
cnf(c_0_77,hypothesis,
least_upper_bound(identity,inverse(X1)) = inverse(greatest_lower_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_74,c_0_18]) ).
cnf(c_0_78,negated_conjecture,
greatest_lower_bound(least_upper_bound(identity,a),least_upper_bound(identity,inverse(a))) != identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_28]),c_0_28]) ).
cnf(c_0_79,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_76,c_0_77]),c_0_23]),c_0_38]),c_0_24]) ).
cnf(c_0_80,negated_conjecture,
greatest_lower_bound(least_upper_bound(identity,a),inverse(greatest_lower_bound(identity,a))) != identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_77]),c_0_24]) ).
cnf(c_0_81,hypothesis,
greatest_lower_bound(least_upper_bound(identity,X1),inverse(greatest_lower_bound(identity,X1))) = identity,
inference(spm,[status(thm)],[c_0_79,c_0_24]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP183-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 00:30:31 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.58 start to proof: theBenchmark
% 2.14/2.18 % Version : CSE_E---1.5
% 2.14/2.18 % Problem : theBenchmark.p
% 2.14/2.18 % Proof found
% 2.14/2.18 % SZS status Theorem for theBenchmark.p
% 2.14/2.18 % SZS output start Proof
% See solution above
% 2.14/2.18 % Total time : 1.585000 s
% 2.14/2.18 % SZS output end Proof
% 2.14/2.18 % Total time : 1.588000 s
%------------------------------------------------------------------------------