TSTP Solution File: GRP167-4 by E-SAT---3.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.2.0
% Problem : GRP167-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d SAT
% Computer : n026.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 : Mon Jun 24 06:52:26 EDT 2024
% Result : Unsatisfiable 2.97s 0.87s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of clauses : 102 ( 102 unt; 0 nHn; 6 RR)
% Number of literals : 102 ( 101 equ; 5 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 174 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',left_identity) ).
cnf(p19_2,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',p19_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/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',monotony_glb1) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',symmetry_of_glb) ).
cnf(p19_3,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',p19_3) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',monotony_lub2) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',symmetry_of_lub) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',lub_absorbtion) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',monotony_lub1) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',monotony_glb2) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',glb_absorbtion) ).
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/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',associativity_of_glb) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',idempotence_of_gld) ).
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/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',associativity_of_lub) ).
cnf(prove_p19,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
file('/export/starexec/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p',prove_p19) ).
cnf(c_0_17,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_18,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_19,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_20,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_21,axiom,
inverse(inverse(X1)) = X1,
p19_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,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),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,axiom,
inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
p19_3 ).
cnf(c_0_26,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_22,c_0_23]),c_0_24]) ).
cnf(c_0_27,plain,
multiply(X1,inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
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,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_21]) ).
cnf(c_0_31,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_26,c_0_18]),c_0_24]) ).
cnf(c_0_32,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_33,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_27]),c_0_19]) ).
cnf(c_0_35,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_36,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_19]),c_0_29]) ).
cnf(c_0_37,plain,
multiply(greatest_lower_bound(X1,identity),inverse(greatest_lower_bound(identity,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_21]) ).
cnf(c_0_38,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_39,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_40,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_21]) ).
cnf(c_0_41,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_35,c_0_20]) ).
cnf(c_0_42,plain,
least_upper_bound(X1,inverse(greatest_lower_bound(identity,inverse(X1)))) = inverse(greatest_lower_bound(identity,inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_29]),c_0_38]),c_0_19]),c_0_29]) ).
cnf(c_0_43,plain,
multiply(greatest_lower_bound(X1,inverse(multiply(X2,X3))),X2) = greatest_lower_bound(multiply(X1,X2),inverse(X3)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
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_41,c_0_42]),c_0_25]),c_0_43]),c_0_19]),c_0_25]),c_0_43]),c_0_19]) ).
cnf(c_0_45,plain,
least_upper_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) = inverse(greatest_lower_bound(X2,X1)),
inference(spm,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_46,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_47,plain,
least_upper_bound(inverse(X1),inverse(least_upper_bound(X1,X2))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_29]) ).
cnf(c_0_48,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_46,c_0_29]) ).
cnf(c_0_49,plain,
least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_21]) ).
cnf(c_0_50,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_38,c_0_48]),c_0_29]) ).
cnf(c_0_51,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_35,c_0_23]),c_0_29]) ).
cnf(c_0_52,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_36,c_0_27]),c_0_29]) ).
cnf(c_0_53,plain,
multiply(inverse(X1),greatest_lower_bound(identity,X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_54,plain,
least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,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_39,c_0_19]),c_0_24]) ).
cnf(c_0_56,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_51,c_0_18]),c_0_29]) ).
cnf(c_0_57,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_58,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld ).
cnf(c_0_59,plain,
greatest_lower_bound(inverse(X1),inverse(multiply(X2,X1))) = multiply(inverse(X1),greatest_lower_bound(identity,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_25]),c_0_24]) ).
cnf(c_0_60,plain,
multiply(least_upper_bound(identity,X1),inverse(X1)) = least_upper_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_29]) ).
cnf(c_0_61,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_46]),c_0_23]) ).
cnf(c_0_62,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = inverse(least_upper_bound(X2,inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_54]),c_0_24]) ).
cnf(c_0_63,plain,
greatest_lower_bound(inverse(X1),inverse(multiply(X1,X2))) = multiply(greatest_lower_bound(identity,inverse(X2)),inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_25]),c_0_24]) ).
cnf(c_0_64,plain,
multiply(inverse(X1),least_upper_bound(identity,X1)) = least_upper_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_56,c_0_29]) ).
cnf(c_0_65,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,plain,
inverse(least_upper_bound(identity,inverse(X1))) = multiply(X1,inverse(least_upper_bound(identity,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_21]),c_0_21]),c_0_61]),c_0_62]) ).
cnf(c_0_67,plain,
inverse(least_upper_bound(identity,inverse(X1))) = multiply(inverse(least_upper_bound(identity,X1)),X1),
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_21]),c_0_61]),c_0_21]),c_0_62]) ).
cnf(c_0_68,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_65]),c_0_18]) ).
cnf(c_0_69,plain,
multiply(inverse(least_upper_bound(identity,X1)),X1) = multiply(X1,inverse(least_upper_bound(identity,X1))),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,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_35,c_0_27]),c_0_29]) ).
cnf(c_0_71,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_72,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(X1,identity))) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_26]),c_0_19]) ).
cnf(c_0_73,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_35,c_0_30]) ).
cnf(c_0_74,plain,
multiply(inverse(least_upper_bound(X1,identity)),X1) = multiply(X1,inverse(least_upper_bound(X1,identity))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_51]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_75,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_76,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_70,c_0_71]) ).
cnf(c_0_77,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_55,c_0_27]),c_0_24]) ).
cnf(c_0_78,plain,
least_upper_bound(inverse(X1),inverse(multiply(X2,X1))) = multiply(inverse(X1),least_upper_bound(identity,inverse(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_25]),c_0_29]) ).
cnf(c_0_79,plain,
least_upper_bound(identity,inverse(greatest_lower_bound(X1,identity))) = inverse(greatest_lower_bound(X1,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_72]),c_0_29]) ).
cnf(c_0_80,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_39,c_0_18]),c_0_24]) ).
cnf(c_0_81,plain,
multiply(least_upper_bound(X1,identity),X1) = multiply(X1,least_upper_bound(X1,identity)),
inference(spm,[status(thm)],[c_0_51,c_0_36]) ).
cnf(c_0_82,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_52]),c_0_76]),c_0_21]),c_0_29]),c_0_71]) ).
cnf(c_0_83,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(spm,[status(thm)],[c_0_77,c_0_24]) ).
cnf(c_0_84,plain,
inverse(greatest_lower_bound(identity,inverse(X1))) = multiply(X1,inverse(greatest_lower_bound(X1,identity))),
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_77]),c_0_21]),c_0_21]),c_0_79]),c_0_44]) ).
cnf(c_0_85,plain,
multiply(greatest_lower_bound(X1,greatest_lower_bound(X2,inverse(X3))),X3) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_80,c_0_57]) ).
cnf(c_0_86,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(fof_simplification,[status(thm)],[prove_p19]) ).
cnf(c_0_87,plain,
multiply(least_upper_bound(identity,X1),X1) = multiply(X1,least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_81,c_0_29]) ).
cnf(c_0_88,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,inverse(X1)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_32]),c_0_29]),c_0_32]),c_0_29]) ).
cnf(c_0_89,plain,
greatest_lower_bound(X1,greatest_lower_bound(identity,multiply(X2,X1))) = greatest_lower_bound(identity,multiply(greatest_lower_bound(X2,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_43,c_0_84]),c_0_21]),c_0_85]),c_0_21]),c_0_24]),c_0_57]) ).
cnf(c_0_90,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
c_0_86 ).
cnf(c_0_91,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_26,c_0_87]),c_0_55]) ).
cnf(c_0_92,plain,
multiply(X1,greatest_lower_bound(X2,inverse(X1))) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_27]),c_0_24]) ).
cnf(c_0_93,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(identity,X1))) = identity,
inference(spm,[status(thm)],[c_0_88,c_0_21]) ).
cnf(c_0_94,plain,
greatest_lower_bound(identity,multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(identity,X1))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_64]),c_0_46]),c_0_24]),c_0_46]),c_0_24]) ).
cnf(c_0_95,negated_conjecture,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_24]),c_0_29]) ).
cnf(c_0_96,plain,
multiply(least_upper_bound(identity,X1),greatest_lower_bound(identity,X1)) = multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)),
inference(spm,[status(thm)],[c_0_91,c_0_24]) ).
cnf(c_0_97,plain,
multiply(X1,multiply(greatest_lower_bound(X2,inverse(X1)),X3)) = multiply(greatest_lower_bound(identity,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_17,c_0_92]) ).
cnf(c_0_98,plain,
multiply(greatest_lower_bound(identity,inverse(X1)),least_upper_bound(identity,X1)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_93]),c_0_24]),c_0_94]) ).
cnf(c_0_99,negated_conjecture,
multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)) != a,
inference(rw,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_100,plain,
multiply(greatest_lower_bound(identity,X1),least_upper_bound(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_23]),c_0_23]) ).
cnf(c_0_101,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP167-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : run_E %s %d SAT
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 20 09:45:54 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.18/0.46 Running first-order model finding
% 0.18/0.46 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.1ZbEaC81Gf/E---3.1_21815.p
% 2.97/0.87 # Version: 3.2.0
% 2.97/0.87 # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.97/0.87 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.97/0.87 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.97/0.87 # Starting new_bool_3 with 300s (1) cores
% 2.97/0.87 # Starting new_bool_1 with 300s (1) cores
% 2.97/0.87 # Starting sh5l with 300s (1) cores
% 2.97/0.87 # sh5l with pid 21896 completed with status 0
% 2.97/0.87 # Result found by sh5l
% 2.97/0.87 # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.97/0.87 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.97/0.87 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.97/0.87 # Starting new_bool_3 with 300s (1) cores
% 2.97/0.87 # Starting new_bool_1 with 300s (1) cores
% 2.97/0.87 # Starting sh5l with 300s (1) cores
% 2.97/0.87 # SinE strategy is gf500_gu_R04_F100_L20000
% 2.97/0.87 # Search class: FUUPM-FFSF21-SFFFFFNN
% 2.97/0.87 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.97/0.87 # Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 2.97/0.87 # U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 21902 completed with status 0
% 2.97/0.87 # Result found by U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 2.97/0.87 # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.97/0.87 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.97/0.87 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.97/0.87 # Starting new_bool_3 with 300s (1) cores
% 2.97/0.87 # Starting new_bool_1 with 300s (1) cores
% 2.97/0.87 # Starting sh5l with 300s (1) cores
% 2.97/0.87 # SinE strategy is gf500_gu_R04_F100_L20000
% 2.97/0.87 # Search class: FUUPM-FFSF21-SFFFFFNN
% 2.97/0.87 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 2.97/0.87 # Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 2.97/0.87 # Preprocessing time : 0.001 s
% 2.97/0.87 # Presaturation interreduction done
% 2.97/0.87
% 2.97/0.87 # Proof found!
% 2.97/0.87 # SZS status Unsatisfiable
% 2.97/0.87 # SZS output start CNFRefutation
% See solution above
% 2.97/0.87 # Parsed axioms : 19
% 2.97/0.87 # Removed by relevancy pruning/SinE : 0
% 2.97/0.87 # Initial clauses : 19
% 2.97/0.87 # Removed in clause preprocessing : 0
% 2.97/0.87 # Initial clauses in saturation : 19
% 2.97/0.87 # Processed clauses : 2136
% 2.97/0.87 # ...of these trivial : 1019
% 2.97/0.87 # ...subsumed : 702
% 2.97/0.87 # ...remaining for further processing : 415
% 2.97/0.87 # Other redundant clauses eliminated : 0
% 2.97/0.87 # Clauses deleted for lack of memory : 0
% 2.97/0.87 # Backward-subsumed : 0
% 2.97/0.87 # Backward-rewritten : 112
% 2.97/0.87 # Generated clauses : 47358
% 2.97/0.87 # ...of the previous two non-redundant : 27409
% 2.97/0.87 # ...aggressively subsumed : 0
% 2.97/0.87 # Contextual simplify-reflections : 0
% 2.97/0.87 # Paramodulations : 47358
% 2.97/0.87 # Factorizations : 0
% 2.97/0.87 # NegExts : 0
% 2.97/0.87 # Equation resolutions : 0
% 2.97/0.87 # Disequality decompositions : 0
% 2.97/0.87 # Total rewrite steps : 75566
% 2.97/0.87 # ...of those cached : 64559
% 2.97/0.87 # Propositional unsat checks : 0
% 2.97/0.87 # Propositional check models : 0
% 2.97/0.87 # Propositional check unsatisfiable : 0
% 2.97/0.87 # Propositional clauses : 0
% 2.97/0.87 # Propositional clauses after purity: 0
% 2.97/0.87 # Propositional unsat core size : 0
% 2.97/0.87 # Propositional preprocessing time : 0.000
% 2.97/0.87 # Propositional encoding time : 0.000
% 2.97/0.87 # Propositional solver time : 0.000
% 2.97/0.87 # Success case prop preproc time : 0.000
% 2.97/0.87 # Success case prop encoding time : 0.000
% 2.97/0.87 # Success case prop solver time : 0.000
% 2.97/0.87 # Current number of processed clauses : 284
% 2.97/0.87 # Positive orientable unit clauses : 272
% 2.97/0.87 # Positive unorientable unit clauses: 12
% 2.97/0.87 # Negative unit clauses : 0
% 2.97/0.87 # Non-unit-clauses : 0
% 2.97/0.87 # Current number of unprocessed clauses: 25205
% 2.97/0.87 # ...number of literals in the above : 25205
% 2.97/0.87 # Current number of archived formulas : 0
% 2.97/0.87 # Current number of archived clauses : 131
% 2.97/0.87 # Clause-clause subsumption calls (NU) : 0
% 2.97/0.87 # Rec. Clause-clause subsumption calls : 0
% 2.97/0.87 # Non-unit clause-clause subsumptions : 0
% 2.97/0.87 # Unit Clause-clause subsumption calls : 62
% 2.97/0.87 # Rewrite failures with RHS unbound : 0
% 2.97/0.87 # BW rewrite match attempts : 1009
% 2.97/0.87 # BW rewrite match successes : 279
% 2.97/0.87 # Condensation attempts : 0
% 2.97/0.87 # Condensation successes : 0
% 2.97/0.87 # Termbank termtop insertions : 531367
% 2.97/0.87 # Search garbage collected termcells : 2
% 2.97/0.87
% 2.97/0.87 # -------------------------------------------------
% 2.97/0.87 # User time : 0.380 s
% 2.97/0.87 # System time : 0.019 s
% 2.97/0.87 # Total time : 0.399 s
% 2.97/0.87 # Maximum resident set size: 1616 pages
% 2.97/0.87
% 2.97/0.87 # -------------------------------------------------
% 2.97/0.87 # User time : 0.381 s
% 2.97/0.87 # System time : 0.020 s
% 2.97/0.87 # Total time : 0.401 s
% 2.97/0.87 # Maximum resident set size: 1688 pages
% 2.97/0.87 % E---3.1 exiting
% 2.97/0.88 % E exiting
%------------------------------------------------------------------------------