%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP177-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:38:51 PM UTC 2026
% Result : Unsatisfiable 188.43s 27.99s
% Output : CNFRefutation 188.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of clauses : 117 ( 117 unt; 0 nHn; 34 RR)
% Number of literals : 117 ( 116 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 169 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
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(p08a_2,hypothesis,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p08a_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/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
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(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(p08a_1,hypothesis,
least_upper_bound(identity,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p08a_1) ).
cnf(p08a_3,hypothesis,
least_upper_bound(identity,c) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p08a_3) ).
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(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(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(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(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(prove_p08a,negated_conjecture,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p08a) ).
cnf(c_0_18,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_19,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_20,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_21,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_22,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_23,hypothesis,
least_upper_bound(identity,b) = b,
p08a_2 ).
cnf(c_0_24,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_25,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
cnf(c_0_26,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_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,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_30,hypothesis,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(b,X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_33,hypothesis,
least_upper_bound(identity,a) = a,
p08a_1 ).
cnf(c_0_34,hypothesis,
least_upper_bound(identity,c) = c,
p08a_3 ).
cnf(c_0_35,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_26,c_0_27]) ).
cnf(c_0_36,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,hypothesis,
least_upper_bound(X1,least_upper_bound(multiply(X1,b),multiply(X1,X2))) = least_upper_bound(multiply(X1,b),multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_29]),c_0_29]),c_0_31]) ).
cnf(c_0_38,hypothesis,
least_upper_bound(X1,multiply(a,X1)) = multiply(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_20]) ).
cnf(c_0_39,hypothesis,
least_upper_bound(identity,least_upper_bound(c,X1)) = least_upper_bound(c,X1),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_40,plain,
greatest_lower_bound(X1,least_upper_bound(X2,least_upper_bound(X1,X3))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_27]) ).
cnf(c_0_41,hypothesis,
least_upper_bound(a,multiply(a,multiply(a,b))) = multiply(a,multiply(a,b)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,hypothesis,
least_upper_bound(X1,least_upper_bound(multiply(X1,c),multiply(X1,X2))) = least_upper_bound(multiply(X1,c),multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_39]),c_0_29]),c_0_29]),c_0_31]) ).
cnf(c_0_43,hypothesis,
greatest_lower_bound(a,least_upper_bound(X1,multiply(a,multiply(a,b)))) = a,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,hypothesis,
least_upper_bound(a,multiply(a,multiply(a,c))) = multiply(a,multiply(a,c)),
inference(spm,[status(thm)],[c_0_42,c_0_38]) ).
cnf(c_0_45,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_46,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_47,hypothesis,
greatest_lower_bound(a,least_upper_bound(multiply(a,multiply(a,b)),X1)) = a,
inference(spm,[status(thm)],[c_0_43,c_0_28]) ).
cnf(c_0_48,hypothesis,
least_upper_bound(X1,multiply(b,X1)) = multiply(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_23]),c_0_20]) ).
cnf(c_0_49,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(greatest_lower_bound(X1,X2),X3))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_50,hypothesis,
greatest_lower_bound(a,multiply(a,multiply(a,c))) = a,
inference(spm,[status(thm)],[c_0_27,c_0_44]) ).
cnf(c_0_51,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,hypothesis,
greatest_lower_bound(a,multiply(a,multiply(a,multiply(a,b)))) = a,
inference(spm,[status(thm)],[c_0_47,c_0_38]) ).
cnf(c_0_53,hypothesis,
greatest_lower_bound(X1,least_upper_bound(X2,multiply(a,X1))) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_38]) ).
cnf(c_0_54,hypothesis,
least_upper_bound(b,multiply(b,multiply(b,c))) = multiply(b,multiply(b,c)),
inference(spm,[status(thm)],[c_0_42,c_0_48]) ).
cnf(c_0_55,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_46]),c_0_26]) ).
cnf(c_0_56,hypothesis,
greatest_lower_bound(X1,multiply(a,X1)) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_57,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(multiply(a,multiply(a,c)),least_upper_bound(a,X1))) = a,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,hypothesis,
least_upper_bound(a,multiply(a,multiply(a,multiply(a,b)))) = multiply(a,multiply(a,multiply(a,b))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_28]) ).
cnf(c_0_59,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_60,hypothesis,
greatest_lower_bound(X1,least_upper_bound(multiply(a,X1),X2)) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_28]) ).
cnf(c_0_61,hypothesis,
least_upper_bound(X1,multiply(X1,b)) = multiply(X1,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_23]),c_0_31]) ).
cnf(c_0_62,hypothesis,
least_upper_bound(X1,multiply(X1,c)) = multiply(X1,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_34]),c_0_31]) ).
cnf(c_0_63,hypothesis,
greatest_lower_bound(b,multiply(b,multiply(b,c))) = b,
inference(spm,[status(thm)],[c_0_27,c_0_54]) ).
cnf(c_0_64,hypothesis,
greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(a,X1))) = greatest_lower_bound(X2,X1),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,hypothesis,
greatest_lower_bound(a,multiply(a,multiply(a,greatest_lower_bound(c,multiply(a,b))))) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_59]) ).
cnf(c_0_66,plain,
greatest_lower_bound(multiply(X1,greatest_lower_bound(X2,X3)),X4) = greatest_lower_bound(multiply(X1,X2),greatest_lower_bound(multiply(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_26,c_0_59]) ).
cnf(c_0_67,hypothesis,
greatest_lower_bound(X1,multiply(a,multiply(X1,b))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_18]) ).
cnf(c_0_68,hypothesis,
greatest_lower_bound(X1,multiply(X1,c)) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_62]) ).
cnf(c_0_69,hypothesis,
greatest_lower_bound(b,greatest_lower_bound(multiply(b,multiply(b,c)),least_upper_bound(b,X1))) = b,
inference(spm,[status(thm)],[c_0_49,c_0_63]) ).
cnf(c_0_70,hypothesis,
least_upper_bound(X1,multiply(X1,a)) = multiply(X1,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_33]),c_0_31]) ).
cnf(c_0_71,hypothesis,
greatest_lower_bound(a,multiply(a,greatest_lower_bound(c,multiply(a,b)))) = a,
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_64,c_0_65]),c_0_66]),c_0_46]),c_0_67]),c_0_46]),c_0_68]) ).
cnf(c_0_72,hypothesis,
greatest_lower_bound(X1,multiply(X1,b)) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_61]) ).
cnf(c_0_73,hypothesis,
greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(b,greatest_lower_bound(X1,X2)))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
cnf(c_0_74,hypothesis,
greatest_lower_bound(b,multiply(b,greatest_lower_bound(a,multiply(b,c)))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_59]),c_0_46]) ).
cnf(c_0_75,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(c,multiply(a,b))) = greatest_lower_bound(a,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_71]),c_0_26]),c_0_46]),c_0_72]),c_0_46]) ).
cnf(c_0_76,hypothesis,
greatest_lower_bound(b,multiply(b,greatest_lower_bound(a,b))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_59]),c_0_26]),c_0_46]),c_0_68]) ).
cnf(c_0_77,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,greatest_lower_bound(X2,X3))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_26]) ).
cnf(c_0_78,hypothesis,
greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(a,greatest_lower_bound(X1,X2)))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_49,c_0_38]) ).
cnf(c_0_79,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(multiply(a,b),multiply(b,greatest_lower_bound(a,c))))) = greatest_lower_bound(a,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_75]),c_0_26]) ).
cnf(c_0_80,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_81,hypothesis,
least_upper_bound(b,multiply(b,greatest_lower_bound(a,b))) = multiply(b,greatest_lower_bound(a,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_76]),c_0_28]) ).
cnf(c_0_82,plain,
least_upper_bound(greatest_lower_bound(X1,X2),greatest_lower_bound(X1,greatest_lower_bound(X3,X2))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_77,c_0_46]) ).
cnf(c_0_83,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(c,greatest_lower_bound(multiply(a,b),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))))) = greatest_lower_bound(a,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_26]),c_0_26]),c_0_80]),c_0_46]) ).
cnf(c_0_84,hypothesis,
greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,b),X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_61]) ).
cnf(c_0_85,hypothesis,
greatest_lower_bound(X1,multiply(b,X1)) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_48]) ).
cnf(c_0_86,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld ).
cnf(c_0_87,hypothesis,
greatest_lower_bound(b,least_upper_bound(X1,multiply(b,greatest_lower_bound(a,b)))) = b,
inference(spm,[status(thm)],[c_0_40,c_0_81]) ).
cnf(c_0_88,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(X3,greatest_lower_bound(X1,X2)))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_89,hypothesis,
least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)))) = greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]),c_0_28]),c_0_84]) ).
cnf(c_0_90,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_45]),c_0_26]) ).
cnf(c_0_91,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X1,X2),X3),X4) = greatest_lower_bound(multiply(X1,X3),greatest_lower_bound(multiply(X2,X3),X4)),
inference(spm,[status(thm)],[c_0_26,c_0_80]) ).
cnf(c_0_92,hypothesis,
greatest_lower_bound(X1,greatest_lower_bound(multiply(b,X1),X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_85]) ).
cnf(c_0_93,hypothesis,
greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,a),X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_70]) ).
cnf(c_0_94,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_86]) ).
cnf(c_0_95,hypothesis,
greatest_lower_bound(b,least_upper_bound(multiply(b,greatest_lower_bound(a,b)),X1)) = b,
inference(spm,[status(thm)],[c_0_87,c_0_28]) ).
cnf(c_0_96,hypothesis,
least_upper_bound(multiply(X1,X2),multiply(X1,multiply(a,X2))) = multiply(X1,multiply(a,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_97,hypothesis,
greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),c)),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]),c_0_66]),c_0_91]),c_0_46]),c_0_55]),c_0_80]),c_0_91]),c_0_55]),c_0_92]),c_0_55]),c_0_93]),c_0_94]) ).
cnf(c_0_98,hypothesis,
greatest_lower_bound(X1,multiply(greatest_lower_bound(a,b),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_56]),c_0_80]) ).
cnf(c_0_99,hypothesis,
greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,c),X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_62]) ).
cnf(c_0_100,hypothesis,
greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(b,X1))) = greatest_lower_bound(X2,X1),
inference(spm,[status(thm)],[c_0_55,c_0_85]) ).
cnf(c_0_101,hypothesis,
greatest_lower_bound(b,multiply(b,multiply(a,greatest_lower_bound(a,b)))) = b,
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_102,hypothesis,
greatest_lower_bound(a,multiply(b,greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),c)),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_97]),c_0_66]),c_0_91]),c_0_59]),c_0_55]),c_0_98]),c_0_91]),c_0_55]),c_0_59]),c_0_94]),c_0_93]),c_0_99]) ).
cnf(c_0_103,plain,
greatest_lower_bound(multiply(X1,X2),greatest_lower_bound(X3,multiply(X1,X4))) = greatest_lower_bound(X3,multiply(X1,greatest_lower_bound(X2,X4))),
inference(spm,[status(thm)],[c_0_55,c_0_59]) ).
cnf(c_0_104,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,multiply(X4,X2))) = multiply(greatest_lower_bound(X1,multiply(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_80,c_0_18]) ).
cnf(c_0_105,hypothesis,
greatest_lower_bound(b,multiply(a,greatest_lower_bound(a,b))) = greatest_lower_bound(b,multiply(a,a)),
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_66]),c_0_46]),c_0_56]),c_0_46]) ).
cnf(c_0_106,hypothesis,
greatest_lower_bound(a,multiply(greatest_lower_bound(b,multiply(a,a)),c)) = greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),c)),
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_78,c_0_102]),c_0_66]),c_0_103]),c_0_104]),c_0_105]),c_0_55]),c_0_93]),c_0_92]) ).
cnf(c_0_107,plain,
greatest_lower_bound(multiply(X1,multiply(X2,X3)),multiply(X4,X3)) = multiply(greatest_lower_bound(multiply(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_80,c_0_18]) ).
cnf(c_0_108,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X3,greatest_lower_bound(X1,X2)),
inference(spm,[status(thm)],[c_0_46,c_0_26]) ).
cnf(c_0_109,hypothesis,
greatest_lower_bound(X1,multiply(X1,a)) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_70]) ).
cnf(c_0_110,hypothesis,
greatest_lower_bound(X1,multiply(a,multiply(X1,c))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_62]),c_0_18]) ).
cnf(c_0_111,negated_conjecture,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(fof_simplification,[status(thm)],[prove_p08a]) ).
cnf(c_0_112,hypothesis,
greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),c)) = greatest_lower_bound(a,multiply(b,c)),
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(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_106]),c_0_91]),c_0_18]),c_0_55]),c_0_107]),c_0_108]),c_0_46]),c_0_109]),c_0_46]),c_0_55]),c_0_80]),c_0_90]),c_0_46]),c_0_91]),c_0_18]),c_0_46]),c_0_110]),c_0_46]) ).
cnf(c_0_113,negated_conjecture,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
c_0_111 ).
cnf(c_0_114,hypothesis,
greatest_lower_bound(a,multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(rw,[status(thm)],[c_0_97,c_0_112]) ).
cnf(c_0_115,negated_conjecture,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) != multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(rw,[status(thm)],[c_0_113,c_0_28]) ).
cnf(c_0_116,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_114]),c_0_115]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP177-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:03:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 188.43/27.99 % Version: 3.5.1
% 188.43/27.99 % Preprocessing class: FSMSSMSSSSSNFFN.
% 188.43/27.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 188.43/27.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 188.43/27.99 % Starting new_bool_3 with 300s (1) cores
% 188.43/27.99 % Starting new_bool_1 with 300s (1) cores
% 188.43/27.99 % Starting sh5l with 300s (1) cores
% 188.43/27.99 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4120466 completed with status 0
% 188.43/27.99 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 188.43/27.99 % Preprocessing class: FSMSSMSSSSSNFFN.
% 188.43/27.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 188.43/27.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 188.43/27.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 188.43/27.99 % No SInE strategy applied
% 188.43/27.99 % Search class: FUUPM-FFSS21-MFFFFFNN
% 188.43/27.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 188.43/27.99 % Starting SubtermCWHack with 136s (1) cores
% 188.43/27.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 188.43/27.99 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 136s (1) cores
% 188.43/27.99 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 188.43/27.99 % Starting G-E--_209_C18_F1_AE_CS_SP_S0Y with 136s (1) cores
% 188.43/27.99 % G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with pid 4120473 completed with status 0
% 188.43/27.99 % Result found by G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN
% 188.43/27.99 % Preprocessing class: FSMSSMSSSSSNFFN.
% 188.43/27.99 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 188.43/27.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 188.43/27.99 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 188.43/27.99 % No SInE strategy applied
% 188.43/27.99 % Search class: FUUPM-FFSS21-MFFFFFNN
% 188.43/27.99 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 188.43/27.99 % Starting SubtermCWHack with 136s (1) cores
% 188.43/27.99 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 188.43/27.99 % Starting G-E--_208_B00_00_F1_SE_CS_SP_PS_S5PRR_S00EN with 136s (1) cores
% 188.43/27.99 % Preprocessing time : 0.002 s
% 188.43/27.99 % Presaturation interreduction done
% 188.43/27.99
% 188.43/27.99 % Proof found!
% 188.43/27.99 % SZS status Unsatisfiable
% 188.43/27.99 % SZS output start CNFRefutation
% See solution above
% 188.43/27.99 % Parsed axioms : 19
% 188.43/27.99 % Removed by relevancy pruning/SinE : 0
% 188.43/27.99 % Initial clauses : 19
% 188.43/27.99 % Removed in clause preprocessing : 0
% 188.43/27.99 % Initial clauses in saturation : 19
% 188.43/27.99 % Processed clauses : 12105
% 188.43/27.99 % ...of these trivial : 2796
% 188.43/27.99 % ...subsumed : 4250
% 188.43/27.99 % ...remaining for further processing : 5059
% 188.43/27.99 % Other redundant clauses eliminated : 0
% 188.43/27.99 % Clauses deleted for lack of memory : 0
% 188.43/27.99 % Backward-subsumed : 0
% 188.43/27.99 % Backward-rewritten : 889
% 188.43/27.99 % Generated clauses : 749926
% 188.43/27.99 % ...of the previous two non-redundant : 416005
% 188.43/27.99 % ...aggressively subsumed : 0
% 188.43/27.99 % Contextual simplify-reflections : 0
% 188.43/27.99 % Paramodulations : 749926
% 188.43/27.99 % Factorizations : 0
% 188.43/27.99 % NegExts : 0
% 188.43/27.99 % Equation resolutions : 0
% 188.43/27.99 % Disequality decompositions : 0
% 188.43/27.99 % Total rewrite steps : 1800469
% 188.43/27.99 % ...of those cached : 1494490
% 188.43/27.99 % Propositional unsat checks : 0
% 188.43/27.99 % Propositional check models : 0
% 188.43/27.99 % Propositional check unsatisfiable : 0
% 188.43/27.99 % Propositional clauses : 0
% 188.43/27.99 % Propositional clauses after purity: 0
% 188.43/27.99 % Propositional unsat core size : 0
% 188.43/27.99 % Propositional preprocessing time : 0.000
% 188.43/27.99 % Propositional encoding time : 0.000
% 188.43/27.99 % Propositional solver time : 0.000
% 188.43/27.99 % Success case prop preproc time : 0.000
% 188.43/27.99 % Success case prop encoding time : 0.000
% 188.43/27.99 % Success case prop solver time : 0.000
% 188.43/27.99 % Current number of processed clauses : 4151
% 188.43/27.99 % Positive orientable unit clauses : 4108
% 188.43/27.99 % Positive unorientable unit clauses: 42
% 188.43/27.99 % Negative unit clauses : 1
% 188.43/27.99 % Non-unit-clauses : 0
% 188.43/27.99 % Current number of unprocessed clauses: 402237
% 188.43/27.99 % ...number of literals in the above : 402237
% 188.43/27.99 % Current number of archived formulas : 0
% 188.43/27.99 % Current number of archived clauses : 908
% 188.43/27.99 % Clause-clause subsumption calls (NU) : 0
% 188.43/27.99 % Rec. Clause-clause subsumption calls : 0
% 188.43/27.99 % Non-unit clause-clause subsumptions : 0
% 188.43/27.99 % Unit Clause-clause subsumption calls : 492
% 188.43/27.99 % Rewrite failures with RHS unbound : 708684
% 188.43/27.99 % BW rewrite match attempts : 152070
% 188.43/27.99 % BW rewrite match successes : 3811
% 188.43/27.99 % Condensation attempts : 0
% 188.43/27.99 % Condensation successes : 0
% 188.43/28.00 % Termbank termtop insertions : 13090177
% 188.43/28.00 % Search garbage collected termcells : 2
% 188.43/28.00
% 188.43/28.00 % -------------------------------------------------
% 188.43/28.00 % User time : 26.207 s
% 188.43/28.00 % System time : 0.700 s
% 188.43/28.00 % Total time : 26.907 s
% 188.43/28.00 % Maximum resident set size: 3640 pages
% 188.43/28.00
% 188.43/28.00 % -------------------------------------------------
% 188.43/28.00 % User time : 128.837 s
% 188.43/28.00 % System time : 4.675 s
% 188.43/28.00 % Total time : 133.512 s
% 188.43/28.00 % Maximum resident set size: 4864 pages
% 188.43/28.00 % E exiting
%------------------------------------------------------------------------------