TSTP Solution File: GRP181-1 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : GRP181-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n019.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 17:46:31 EDT 2023
% Result : Unsatisfiable 37.00s 5.07s
% Output : CNFRefutation 37.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 16
% Syntax : Number of clauses : 118 ( 118 unt; 0 nHn; 15 RR)
% Number of literals : 118 ( 117 equ; 2 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 : 214 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',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/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',monotony_glb1) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',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/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',monotony_lub2) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',symmetry_of_lub) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',glb_absorbtion) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',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/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',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/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',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/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',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/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',monotony_lub1) ).
cnf(p12_2,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox2/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',p12_2) ).
cnf(p12_1,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox2/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p',p12_1) ).
cnf(prove_p12,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/tmp/tmp.4lSR28Ef4s/E---3.1_2686.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
% 0.09/0.10 % Problem : GRP181-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n019.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 2400
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Oct 3 02:33:21 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.41 Running first-order model finding
% 0.16/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.4lSR28Ef4s/E---3.1_2686.p
% 37.00/5.07 # Version: 3.1pre001
% 37.00/5.07 # Preprocessing class: FSMSSMSSSSSNFFN.
% 37.00/5.07 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.00/5.07 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 37.00/5.07 # Starting new_bool_3 with 300s (1) cores
% 37.00/5.07 # Starting new_bool_1 with 300s (1) cores
% 37.00/5.07 # Starting sh5l with 300s (1) cores
% 37.00/5.07 # sh5l with pid 2766 completed with status 0
% 37.00/5.07 # Result found by sh5l
% 37.00/5.07 # Preprocessing class: FSMSSMSSSSSNFFN.
% 37.00/5.07 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.00/5.07 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 37.00/5.07 # Starting new_bool_3 with 300s (1) cores
% 37.00/5.07 # Starting new_bool_1 with 300s (1) cores
% 37.00/5.07 # Starting sh5l with 300s (1) cores
% 37.00/5.07 # SinE strategy is gf500_gu_R04_F100_L20000
% 37.00/5.07 # Search class: FUUPM-FFSF21-SFFFFFNN
% 37.00/5.07 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 37.00/5.07 # Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 37.00/5.07 # U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2773 completed with status 0
% 37.00/5.07 # Result found by U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 37.00/5.07 # Preprocessing class: FSMSSMSSSSSNFFN.
% 37.00/5.07 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.00/5.07 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 37.00/5.07 # Starting new_bool_3 with 300s (1) cores
% 37.00/5.07 # Starting new_bool_1 with 300s (1) cores
% 37.00/5.07 # Starting sh5l with 300s (1) cores
% 37.00/5.07 # SinE strategy is gf500_gu_R04_F100_L20000
% 37.00/5.07 # Search class: FUUPM-FFSF21-SFFFFFNN
% 37.00/5.07 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 37.00/5.07 # Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 37.00/5.07 # Preprocessing time : 0.001 s
% 37.00/5.07 # Presaturation interreduction done
% 37.00/5.07
% 37.00/5.07 # Proof found!
% 37.00/5.07 # SZS status Unsatisfiable
% 37.00/5.07 # SZS output start CNFRefutation
% See solution above
% 37.00/5.07 # Parsed axioms : 18
% 37.00/5.07 # Removed by relevancy pruning/SinE : 0
% 37.00/5.07 # Initial clauses : 18
% 37.00/5.07 # Removed in clause preprocessing : 0
% 37.00/5.07 # Initial clauses in saturation : 18
% 37.00/5.07 # Processed clauses : 25105
% 37.00/5.07 # ...of these trivial : 11919
% 37.00/5.07 # ...subsumed : 11727
% 37.00/5.07 # ...remaining for further processing : 1459
% 37.00/5.07 # Other redundant clauses eliminated : 0
% 37.00/5.07 # Clauses deleted for lack of memory : 0
% 37.00/5.07 # Backward-subsumed : 0
% 37.00/5.07 # Backward-rewritten : 377
% 37.00/5.07 # Generated clauses : 430159
% 37.00/5.07 # ...of the previous two non-redundant : 253389
% 37.00/5.07 # ...aggressively subsumed : 0
% 37.00/5.07 # Contextual simplify-reflections : 0
% 37.00/5.07 # Paramodulations : 430159
% 37.00/5.07 # Factorizations : 0
% 37.00/5.07 # NegExts : 0
% 37.00/5.07 # Equation resolutions : 0
% 37.00/5.07 # Total rewrite steps : 798884
% 37.00/5.07 # Propositional unsat checks : 0
% 37.00/5.07 # Propositional check models : 0
% 37.00/5.07 # Propositional check unsatisfiable : 0
% 37.00/5.07 # Propositional clauses : 0
% 37.00/5.07 # Propositional clauses after purity: 0
% 37.00/5.07 # Propositional unsat core size : 0
% 37.00/5.07 # Propositional preprocessing time : 0.000
% 37.00/5.07 # Propositional encoding time : 0.000
% 37.00/5.07 # Propositional solver time : 0.000
% 37.00/5.07 # Success case prop preproc time : 0.000
% 37.00/5.07 # Success case prop encoding time : 0.000
% 37.00/5.07 # Success case prop solver time : 0.000
% 37.00/5.07 # Current number of processed clauses : 1064
% 37.00/5.07 # Positive orientable unit clauses : 1047
% 37.00/5.07 # Positive unorientable unit clauses: 16
% 37.00/5.07 # Negative unit clauses : 1
% 37.00/5.07 # Non-unit-clauses : 0
% 37.00/5.07 # Current number of unprocessed clauses: 227542
% 37.00/5.07 # ...number of literals in the above : 227542
% 37.00/5.07 # Current number of archived formulas : 0
% 37.00/5.07 # Current number of archived clauses : 395
% 37.00/5.07 # Clause-clause subsumption calls (NU) : 0
% 37.00/5.07 # Rec. Clause-clause subsumption calls : 0
% 37.00/5.07 # Non-unit clause-clause subsumptions : 0
% 37.00/5.07 # Unit Clause-clause subsumption calls : 131
% 37.00/5.07 # Rewrite failures with RHS unbound : 0
% 37.00/5.07 # BW rewrite match attempts : 6954
% 37.00/5.07 # BW rewrite match successes : 900
% 37.00/5.07 # Condensation attempts : 0
% 37.00/5.07 # Condensation successes : 0
% 37.00/5.07 # Termbank termtop insertions : 5987420
% 37.00/5.07
% 37.00/5.07 # -------------------------------------------------
% 37.00/5.07 # User time : 4.378 s
% 37.00/5.07 # System time : 0.194 s
% 37.00/5.07 # Total time : 4.573 s
% 37.00/5.07 # Maximum resident set size: 1624 pages
% 37.00/5.07
% 37.00/5.07 # -------------------------------------------------
% 37.00/5.07 # User time : 4.380 s
% 37.00/5.07 # System time : 0.196 s
% 37.00/5.07 # Total time : 4.576 s
% 37.00/5.07 # Maximum resident set size: 1676 pages
% 37.00/5.07 % E---3.1 exiting
%------------------------------------------------------------------------------