TSTP Solution File: GRP181-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP181-1 : 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 : n005.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 00:17:32 EDT 2023
% Result : Unsatisfiable 2.76s 2.95s
% Output : CNFRefutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 24
% Syntax : Number of formulae : 126 ( 118 unt; 8 typ; 0 def)
% Number of atoms : 118 ( 117 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 214 ( 10 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
identity: $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
inverse: $i > $i ).
tff(decl_25,type,
greatest_lower_bound: ( $i * $i ) > $i ).
tff(decl_26,type,
least_upper_bound: ( $i * $i ) > $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
c: $i ).
tff(decl_29,type,
b: $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_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_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(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(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(monotony_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(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(associativity_of_glb,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(monotony_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(p12_2,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_2) ).
cnf(p12_1,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_1) ).
cnf(prove_p12,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p12) ).
cnf(c_0_16,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_17,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_18,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_19,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_20,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_21,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_22,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).
cnf(c_0_24,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_25,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_26,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_27,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = identity,
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_28,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_29,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_30,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_25,c_0_22]),c_0_26]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_32,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_27]),c_0_22]) ).
cnf(c_0_33,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_28,c_0_18]),c_0_29]) ).
cnf(c_0_34,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_30,c_0_17]),c_0_26]) ).
cnf(c_0_35,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_36,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
multiply(least_upper_bound(X1,identity),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_24]),c_0_29]) ).
cnf(c_0_38,plain,
multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_39,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_29]) ).
cnf(c_0_40,plain,
multiply(X1,inverse(least_upper_bound(X1,identity))) = inverse(least_upper_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(X1,identity))) = inverse(least_upper_bound(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_22]) ).
cnf(c_0_42,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_32]),c_0_23]) ).
cnf(c_0_43,plain,
multiply(inverse(X1),greatest_lower_bound(multiply(X1,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X1),X3)),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_44,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(identity,inverse(X1)))) = inverse(least_upper_bound(identity,inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_40]),c_0_26]),c_0_41]),c_0_40]) ).
cnf(c_0_45,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_32]) ).
cnf(c_0_46,plain,
multiply(least_upper_bound(X1,inverse(multiply(X2,X3))),X2) = least_upper_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_47,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_48,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_49,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = inverse(least_upper_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_43,c_0_44]),c_0_45]),c_0_46]),c_0_18]),c_0_45]),c_0_46]),c_0_18]) ).
cnf(c_0_50,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_51,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_26]) ).
cnf(c_0_52,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_48,c_0_18]),c_0_26]) ).
cnf(c_0_53,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_54,plain,
multiply(greatest_lower_bound(inverse(multiply(X1,X2)),X3),X1) = greatest_lower_bound(inverse(X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_42]) ).
cnf(c_0_55,plain,
greatest_lower_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(least_upper_bound(X2,X1)),
inference(spm,[status(thm)],[c_0_49,c_0_23]) ).
cnf(c_0_56,plain,
multiply(inverse(identity),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_57,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_58,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_50,c_0_51]) ).
cnf(c_0_59,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_52,c_0_24]),c_0_26]) ).
cnf(c_0_60,plain,
greatest_lower_bound(multiply(X1,X2),greatest_lower_bound(multiply(X3,X2),X4)) = greatest_lower_bound(multiply(greatest_lower_bound(X1,X3),X2),X4),
inference(spm,[status(thm)],[c_0_53,c_0_48]) ).
cnf(c_0_61,plain,
multiply(greatest_lower_bound(multiply(X1,X2),X3),inverse(X2)) = greatest_lower_bound(X1,multiply(X3,inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_45]),c_0_23]),c_0_23]) ).
cnf(c_0_62,plain,
multiply(X1,greatest_lower_bound(inverse(X1),X2)) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_63,plain,
greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X1,X2))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_47]),c_0_26]) ).
cnf(c_0_64,plain,
multiply(inverse(inverse(identity)),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_56]) ).
cnf(c_0_65,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_22]),c_0_29]) ).
cnf(c_0_66,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_53,c_0_35]) ).
cnf(c_0_67,plain,
greatest_lower_bound(least_upper_bound(X1,X2),least_upper_bound(greatest_lower_bound(X3,X1),X2)) = least_upper_bound(greatest_lower_bound(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_58]),c_0_26]) ).
cnf(c_0_68,plain,
multiply(X1,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_36,c_0_59]) ).
cnf(c_0_69,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X1,X2),inverse(X1)),X3) = greatest_lower_bound(identity,greatest_lower_bound(multiply(X2,inverse(X1)),X3)),
inference(spm,[status(thm)],[c_0_60,c_0_24]) ).
cnf(c_0_70,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_39,c_0_51]),c_0_26]) ).
cnf(c_0_71,plain,
multiply(X1,inverse(greatest_lower_bound(multiply(X2,X1),X3))) = inverse(greatest_lower_bound(X2,multiply(X3,inverse(X1)))),
inference(spm,[status(thm)],[c_0_36,c_0_61]) ).
cnf(c_0_72,plain,
greatest_lower_bound(identity,multiply(X1,inverse(greatest_lower_bound(X1,X2)))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_24]) ).
cnf(c_0_73,plain,
inverse(identity) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_64]) ).
cnf(c_0_74,plain,
multiply(least_upper_bound(X1,identity),X1) = multiply(X1,least_upper_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_65,c_0_33]) ).
cnf(c_0_75,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_57,c_0_19]) ).
cnf(c_0_76,plain,
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_66,c_0_30]) ).
cnf(c_0_77,plain,
multiply(least_upper_bound(identity,inverse(X1)),greatest_lower_bound(X1,identity)) = least_upper_bound(greatest_lower_bound(X1,identity),greatest_lower_bound(identity,inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]) ).
cnf(c_0_78,plain,
greatest_lower_bound(X1,least_upper_bound(greatest_lower_bound(X2,X1),greatest_lower_bound(X1,X3))) = least_upper_bound(greatest_lower_bound(X2,X1),greatest_lower_bound(X1,X3)),
inference(spm,[status(thm)],[c_0_67,c_0_47]) ).
cnf(c_0_79,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_28,c_0_17]),c_0_29]) ).
cnf(c_0_80,plain,
multiply(least_upper_bound(inverse(multiply(X1,X2)),X3),X1) = least_upper_bound(inverse(X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
cnf(c_0_81,plain,
multiply(greatest_lower_bound(X1,X2),inverse(greatest_lower_bound(X2,X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_16]),c_0_71]),c_0_23]),c_0_18]),c_0_36]),c_0_72]),c_0_73]) ).
cnf(c_0_82,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_74,c_0_29]) ).
cnf(c_0_83,plain,
multiply(X1,least_upper_bound(X2,greatest_lower_bound(identity,inverse(X1)))) = least_upper_bound(greatest_lower_bound(identity,X1),multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_38]),c_0_23]),c_0_23]),c_0_29]) ).
cnf(c_0_84,plain,
least_upper_bound(greatest_lower_bound(X1,identity),greatest_lower_bound(identity,inverse(X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_79]),c_0_18]),c_0_35]) ).
cnf(c_0_85,plain,
least_upper_bound(greatest_lower_bound(X1,X2),multiply(X3,greatest_lower_bound(X2,X1))) = multiply(least_upper_bound(identity,X3),greatest_lower_bound(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_73]),c_0_23]) ).
cnf(c_0_86,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(X1,identity)) = multiply(greatest_lower_bound(X1,identity),least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_82]),c_0_52]) ).
cnf(c_0_87,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_42,c_0_31]) ).
cnf(c_0_88,plain,
multiply(inverse(X1),least_upper_bound(X1,identity)) = least_upper_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_17]),c_0_29]) ).
cnf(c_0_89,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_57,c_0_24]),c_0_29]) ).
cnf(c_0_90,plain,
multiply(greatest_lower_bound(X1,identity),least_upper_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_22]),c_0_85]),c_0_86]) ).
cnf(c_0_91,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_57,c_0_32]) ).
cnf(c_0_92,plain,
multiply(inverse(least_upper_bound(X1,identity)),X1) = inverse(least_upper_bound(identity,inverse(X1))),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_93,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_89,c_0_50]) ).
cnf(c_0_94,plain,
inverse(least_upper_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_90]),c_0_34]) ).
cnf(c_0_95,plain,
least_upper_bound(X1,least_upper_bound(identity,multiply(X1,X2))) = least_upper_bound(identity,multiply(X1,least_upper_bound(X2,identity))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_23]),c_0_93]),c_0_23]),c_0_29]),c_0_50]) ).
cnf(c_0_96,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_51,c_0_39]),c_0_29]) ).
cnf(c_0_97,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_47]),c_0_26]) ).
cnf(c_0_98,plain,
least_upper_bound(multiply(X1,X2),least_upper_bound(multiply(X1,X3),X4)) = least_upper_bound(multiply(X1,least_upper_bound(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_50,c_0_57]) ).
cnf(c_0_99,plain,
multiply(greatest_lower_bound(inverse(X1),X2),X1) = greatest_lower_bound(identity,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_17]) ).
cnf(c_0_100,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)),
inference(spm,[status(thm)],[c_0_49,c_0_29]) ).
cnf(c_0_101,plain,
inverse(least_upper_bound(X1,identity)) = greatest_lower_bound(identity,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_18]),c_0_96]),c_0_18]),c_0_94]),c_0_97]) ).
cnf(c_0_102,plain,
least_upper_bound(multiply(inverse(X1),least_upper_bound(X1,X2)),X3) = least_upper_bound(identity,least_upper_bound(multiply(inverse(X1),X2),X3)),
inference(spm,[status(thm)],[c_0_98,c_0_17]) ).
cnf(c_0_103,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_51,c_0_35]),c_0_29]) ).
cnf(c_0_104,plain,
greatest_lower_bound(identity,multiply(inverse(least_upper_bound(X1,X2)),X1)) = multiply(inverse(least_upper_bound(X1,X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_23]),c_0_23]) ).
cnf(c_0_105,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c),
p12_2 ).
cnf(c_0_106,plain,
multiply(inverse(least_upper_bound(X1,X2)),X1) = greatest_lower_bound(identity,multiply(inverse(X2),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_101,c_0_102]),c_0_29]),c_0_103]),c_0_94]),c_0_87]),c_0_87]),c_0_104]) ).
cnf(c_0_107,hypothesis,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_29]),c_0_29]) ).
cnf(c_0_108,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
p12_1 ).
cnf(c_0_109,plain,
multiply(inverse(X1),greatest_lower_bound(X2,multiply(X1,X3))) = greatest_lower_bound(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_110,hypothesis,
greatest_lower_bound(identity,multiply(inverse(a),c)) = greatest_lower_bound(identity,multiply(inverse(b),c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_106]) ).
cnf(c_0_111,hypothesis,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_26]),c_0_26]) ).
cnf(c_0_112,hypothesis,
multiply(a,greatest_lower_bound(identity,multiply(inverse(b),c))) = greatest_lower_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_23]),c_0_23]),c_0_22]),c_0_26]),c_0_111]) ).
cnf(c_0_113,hypothesis,
greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(a),greatest_lower_bound(c,b)),
inference(spm,[status(thm)],[c_0_19,c_0_112]) ).
cnf(c_0_114,hypothesis,
multiply(b,multiply(inverse(a),greatest_lower_bound(c,b))) = greatest_lower_bound(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_113]),c_0_23]),c_0_23]),c_0_22]),c_0_26]) ).
cnf(c_0_115,hypothesis,
inverse(a) = inverse(b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_114]),c_0_16]),c_0_24]),c_0_22]) ).
cnf(c_0_116,negated_conjecture,
a != b,
prove_p12 ).
cnf(c_0_117,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_115]),c_0_23]),c_0_116]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP181-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n005.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 22:17:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 2.76/2.95 % Version : CSE_E---1.5
% 2.76/2.95 % Problem : theBenchmark.p
% 2.76/2.95 % Proof found
% 2.76/2.95 % SZS status Theorem for theBenchmark.p
% 2.76/2.95 % SZS output start Proof
% See solution above
% 2.76/2.95 % Total time : 2.367000 s
% 2.76/2.95 % SZS output end Proof
% 2.76/2.95 % Total time : 2.370000 s
%------------------------------------------------------------------------------