%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 : Sun Sep 27 07:28:11 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 70 ( 70 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(symmetry_of_glb,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,VAR_1) = greatest_lower_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_glb) ).
cnf(c_4,plain,
greatest_lower_bound(A,B) = greatest_lower_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_glb]) ).
fof(symmetry_of_lub,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,VAR_1) = least_upper_bound(VAR_1,VAR_0),
file('theBenchmark.p',symmetry_of_lub) ).
cnf(c_5,plain,
least_upper_bound(A,B) = least_upper_bound(B,A),
inference(clausify,[status(thm)],[symmetry_of_lub]) ).
fof(monotony_lub1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,least_upper_bound(VAR_1,VAR_2)) = least_upper_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_lub1) ).
cnf(c_14,plain,
multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_lub1]) ).
cnf(c_15,plain,
least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)),
inference(copy,[status(thm)],[c_14]) ).
fof(monotony_glb1,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',monotony_glb1) ).
cnf(c_16,plain,
multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[monotony_glb1]) ).
cnf(c_17,plain,
greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_16]) ).
fof(monotony_lub2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(least_upper_bound(VAR_0,VAR_1),VAR_2) = least_upper_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_lub2) ).
cnf(c_18,plain,
multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_lub2]) ).
cnf(c_19,plain,
least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B),
inference(copy,[status(thm)],[c_18]) ).
fof(monotony_glb2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(greatest_lower_bound(VAR_0,VAR_1),VAR_2) = greatest_lower_bound(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2)),
file('theBenchmark.p',monotony_glb2) ).
cnf(c_20,plain,
multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)),
inference(clausify,[status(thm)],[monotony_glb2]) ).
cnf(c_21,plain,
greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B),
inference(copy,[status(thm)],[c_20]) ).
fof(p10,axiom,
! [VAR_0,VAR_1] : inverse(least_upper_bound(VAR_0,VAR_1)) = greatest_lower_bound(inverse(VAR_0),inverse(VAR_1)),
file('theBenchmark.p',p10) ).
cnf(c_22,plain,
inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)),
inference(clausify,[status(thm)],[p10]) ).
fof(lat4_1,axiom,
! [VAR_0] : positive_part(VAR_0) = least_upper_bound(VAR_0,identity),
file('theBenchmark.p',lat4_1) ).
cnf(c_23,plain,
positive_part(A) = least_upper_bound(A,identity),
inference(clausify,[status(thm)],[lat4_1]) ).
fof(lat4_2,axiom,
! [VAR_0] : negative_part(VAR_0) = greatest_lower_bound(VAR_0,identity),
file('theBenchmark.p',lat4_2) ).
cnf(c_24,plain,
negative_part(A) = greatest_lower_bound(A,identity),
inference(clausify,[status(thm)],[lat4_2]) ).
fof(prove_lat4,axiom,
a != multiply(positive_part(a),negative_part(a)),
file('theBenchmark.p',prove_lat4) ).
cnf(c_28,plain,
a != multiply(positive_part(a),negative_part(a)),
inference(clausify,[status(thm)],[prove_lat4]) ).
cnf(c_408,plain,
a != multiply(least_upper_bound(a,identity),negative_part(a)),
inference(paramod,[status(thm)],[c_23,c_28]) ).
cnf(c_409,plain,
a != multiply(least_upper_bound(identity,a),negative_part(a)),
inference(paramod,[status(thm)],[c_5,c_408]) ).
cnf(c_410,plain,
a != multiply(least_upper_bound(identity,a),greatest_lower_bound(a,identity)),
inference(paramod,[status(thm)],[c_24,c_409]) ).
cnf(c_411,plain,
a != multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)),
inference(paramod,[status(thm)],[c_4,c_410]) ).
cnf(c_29,plain,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(copy,[status(thm)],[c_411]) ).
cnf(c_412,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_413,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_412]) ).
cnf(c_30,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_413]) ).
cnf(c_52,plain,
least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_59,plain,
greatest_lower_bound(A,multiply(B,A)) = multiply(greatest_lower_bound(identity,B),A),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_83,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_30]) ).
cnf(c_94,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_30,c_30]) ).
cnf(c_95,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_94,c_83]) ).
cnf(c_104,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_95,c_2]) ).
cnf(c_105,plain,
least_upper_bound(A,multiply(A,B)) = multiply(A,least_upper_bound(identity,B)),
inference(paramod,[status(thm)],[c_95,c_15]) ).
cnf(c_107,plain,
greatest_lower_bound(A,multiply(A,B)) = multiply(A,greatest_lower_bound(identity,B)),
inference(paramod,[status(thm)],[c_95,c_17]) ).
cnf(c_414,plain,
multiply(A,least_upper_bound(identity,A)) = multiply(least_upper_bound(identity,A),A),
inference(paramod,[status(thm)],[c_105,c_52]) ).
cnf(c_224,plain,
multiply(least_upper_bound(identity,A),A) = multiply(A,least_upper_bound(identity,A)),
inference(copy,[status(thm)],[c_414]) ).
cnf(c_415,plain,
greatest_lower_bound(inverse(A),identity) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_2,c_107]) ).
cnf(c_259,plain,
greatest_lower_bound(identity,inverse(A)) = multiply(inverse(A),greatest_lower_bound(identity,A)),
inference(paramod,[status(thm)],[c_4,c_415]) ).
cnf(c_416,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(least_upper_bound(identity,a),a)) != a,
inference(paramod,[status(thm)],[c_107,c_29]) ).
cnf(c_417,plain,
greatest_lower_bound(least_upper_bound(identity,a),multiply(a,least_upper_bound(identity,a))) != a,
inference(paramod,[status(thm)],[c_224,c_416]) ).
cnf(c_273,plain,
multiply(greatest_lower_bound(identity,a),least_upper_bound(identity,a)) != a,
inference(paramod,[status(thm)],[c_59,c_417]) ).
cnf(c_275,plain,
greatest_lower_bound(inverse(A),B) = multiply(inverse(A),greatest_lower_bound(identity,multiply(A,B))),
inference(paramod,[status(thm)],[c_30,c_107]) ).
cnf(c_418,plain,
multiply(A,greatest_lower_bound(identity,A)) = multiply(greatest_lower_bound(identity,A),A),
inference(paramod,[status(thm)],[c_107,c_59]) ).
cnf(c_280,plain,
multiply(greatest_lower_bound(identity,A),A) = multiply(A,greatest_lower_bound(identity,A)),
inference(copy,[status(thm)],[c_418]) ).
cnf(c_300,plain,
inverse(least_upper_bound(A,B)) = multiply(inverse(A),greatest_lower_bound(identity,multiply(A,inverse(B)))),
inference(paramod,[status(thm)],[c_275,c_22]) ).
cnf(c_419,plain,
multiply(inverse(least_upper_bound(identity,A)),multiply(A,least_upper_bound(identity,A))) = A,
inference(paramod,[status(thm)],[c_224,c_30]) ).
cnf(c_420,plain,
multiply(multiply(inverse(identity),greatest_lower_bound(identity,multiply(identity,inverse(A)))),multiply(A,least_upper_bound(identity,A))) = A,
inference(paramod,[status(thm)],[c_300,c_419]) ).
cnf(c_421,plain,
multiply(multiply(identity,greatest_lower_bound(identity,multiply(identity,inverse(A)))),multiply(A,least_upper_bound(identity,A))) = A,
inference(paramod,[status(thm)],[c_104,c_420]) ).
cnf(c_422,plain,
multiply(multiply(identity,greatest_lower_bound(identity,inverse(A))),multiply(A,least_upper_bound(identity,A))) = A,
inference(paramod,[status(thm)],[c_1,c_421]) ).
cnf(c_423,plain,
multiply(multiply(identity,multiply(inverse(A),greatest_lower_bound(identity,A))),multiply(A,least_upper_bound(identity,A))) = A,
inference(paramod,[status(thm)],[c_259,c_422]) ).
cnf(c_424,plain,
multiply(multiply(inverse(A),greatest_lower_bound(identity,A)),multiply(A,least_upper_bound(identity,A))) = A,
inference(paramod,[status(thm)],[c_1,c_423]) ).
cnf(c_375,plain,
multiply(inverse(A),multiply(greatest_lower_bound(identity,A),multiply(A,least_upper_bound(identity,A)))) = A,
inference(paramod,[status(thm)],[c_3,c_424]) ).
cnf(c_425,plain,
multiply(multiply(A,greatest_lower_bound(identity,A)),B) = multiply(greatest_lower_bound(identity,A),multiply(A,B)),
inference(paramod,[status(thm)],[c_280,c_3]) ).
cnf(c_426,plain,
multiply(A,multiply(greatest_lower_bound(identity,A),B)) = multiply(greatest_lower_bound(identity,A),multiply(A,B)),
inference(paramod,[status(thm)],[c_3,c_425]) ).
cnf(c_395,plain,
multiply(greatest_lower_bound(identity,A),multiply(A,B)) = multiply(A,multiply(greatest_lower_bound(identity,A),B)),
inference(copy,[status(thm)],[c_426]) ).
cnf(c_427,plain,
multiply(inverse(A),multiply(A,multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)))) = A,
inference(paramod,[status(thm)],[c_395,c_375]) ).
cnf(c_406,plain,
multiply(greatest_lower_bound(identity,A),least_upper_bound(identity,A)) = A,
inference(paramod,[status(thm)],[c_30,c_427]) ).
cnf(c_407,plain,
$false,
inference(resolve,[status(thm)],[c_406,c_273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:33:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1272017 was started by sandbox on n008,
% 0.09/0.36 % Fri Sep 25 14:33:54 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.45
% 0.13/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.45
% 0.13/0.45 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.13/0.45 % Length of proof is 37.
% 0.13/0.45 % Level of proof is 9.
% 0.13/0.45 % Maximum clause weight is 49.000.
% 0.13/0.45 % Given clauses 46.
% 0.13/0.45
% 0.13/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------