%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP172-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:28:13 AM UTC 2026
% Result : Unsatisfiable 0.22s 5.52s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 44 unt; 0 def)
% Number of atoms : 44 ( 43 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 3 sgn 19 !; 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(associativity_of_glb,axiom,
! [VAR_0,VAR_1,VAR_2] : greatest_lower_bound(VAR_0,greatest_lower_bound(VAR_1,VAR_2)) = greatest_lower_bound(greatest_lower_bound(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',associativity_of_glb) ).
cnf(c_6,plain,
greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C),
inference(clausify,[status(thm)],[associativity_of_glb]) ).
cnf(c_7,plain,
greatest_lower_bound(greatest_lower_bound(A,B),C) = greatest_lower_bound(A,greatest_lower_bound(B,C)),
inference(copy,[status(thm)],[c_6]) ).
fof(lub_absorbtion,axiom,
! [VAR_0,VAR_1] : least_upper_bound(VAR_0,greatest_lower_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',lub_absorbtion) ).
cnf(c_12,plain,
least_upper_bound(A,greatest_lower_bound(A,B)) = A,
inference(clausify,[status(thm)],[lub_absorbtion]) ).
fof(glb_absorbtion,axiom,
! [VAR_0,VAR_1] : greatest_lower_bound(VAR_0,least_upper_bound(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',glb_absorbtion) ).
cnf(c_13,plain,
greatest_lower_bound(A,least_upper_bound(A,B)) = A,
inference(clausify,[status(thm)],[glb_absorbtion]) ).
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(p04b_1,axiom,
greatest_lower_bound(identity,a) = identity,
file('theBenchmark.p',p04b_1) ).
cnf(c_22,plain,
greatest_lower_bound(identity,a) = identity,
inference(clausify,[status(thm)],[p04b_1]) ).
fof(p04b_2,axiom,
greatest_lower_bound(identity,b) = identity,
file('theBenchmark.p',p04b_2) ).
cnf(c_23,plain,
greatest_lower_bound(identity,b) = identity,
inference(clausify,[status(thm)],[p04b_2]) ).
fof(prove_p04b,axiom,
greatest_lower_bound(identity,multiply(a,b)) != identity,
file('theBenchmark.p',prove_p04b) ).
cnf(c_24,plain,
greatest_lower_bound(identity,multiply(a,b)) != identity,
inference(clausify,[status(thm)],[prove_p04b]) ).
cnf(c_285,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_286,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_285]) ).
cnf(c_25,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_286]) ).
cnf(c_36,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_12]) ).
cnf(c_287,plain,
greatest_lower_bound(identity,A) = greatest_lower_bound(identity,greatest_lower_bound(a,A)),
inference(paramod,[status(thm)],[c_22,c_7]) ).
cnf(c_64,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,A)) = greatest_lower_bound(identity,A),
inference(copy,[status(thm)],[c_287]) ).
cnf(c_71,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_25]) ).
cnf(c_81,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_25,c_25]) ).
cnf(c_82,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_81,c_71]) ).
cnf(c_288,plain,
least_upper_bound(b,identity) = b,
inference(paramod,[status(thm)],[c_23,c_36]) ).
cnf(c_92,plain,
least_upper_bound(identity,b) = b,
inference(paramod,[status(thm)],[c_5,c_288]) ).
cnf(c_289,plain,
least_upper_bound(multiply(A,identity),multiply(A,b)) = multiply(A,b),
inference(paramod,[status(thm)],[c_92,c_15]) ).
cnf(c_99,plain,
least_upper_bound(A,multiply(A,b)) = multiply(A,b),
inference(paramod,[status(thm)],[c_82,c_289]) ).
cnf(c_151,plain,
greatest_lower_bound(A,multiply(A,b)) = A,
inference(paramod,[status(thm)],[c_99,c_13]) ).
cnf(c_290,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_151,c_64]) ).
cnf(c_291,plain,
identity = greatest_lower_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_22,c_290]) ).
cnf(c_292,plain,
greatest_lower_bound(identity,multiply(a,b)) = identity,
inference(copy,[status(thm)],[c_291]) ).
cnf(c_284,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP172-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.45 % Computer : n015.cluster.edu
% 0.16/5.45 % Model : x86_64 x86_64
% 0.16/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.45 % Memory : 8046.5625MB
% 0.16/5.45 % OS : Linux 6.8.0-71-generic
% 0.16/5.45 % CPULimit : 300
% 0.16/5.45 % WCLimit : 300
% 0.16/5.45 % DateTime : Fri Sep 25 14:37:02 UTC 2026
% 0.16/5.46 % CPUTime :
% 0.16/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.46 % Process 1601711 was started by sandbox2 on n015,
% 0.16/5.46 % Fri Sep 25 14:37:02 2026
% 0.16/5.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.46
% 0.16/5.46 % From the command line: assign(max_seconds, 300).
% 0.22/5.52
% 0.22/5.52 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.22/5.52
% 0.22/5.52 % SZS status Unsatisfiable for theBenchmark
% 0.22/5.52
% 0.22/5.52 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.22/5.52 % Length of proof is 24.
% 0.22/5.52 % Level of proof is 6.
% 0.22/5.52 % Maximum clause weight is 31.000.
% 0.22/5.52 % Given clauses 49.
% 0.22/5.52
% 0.22/5.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------