%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP172-2 : 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 : n001.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 0.13s 0.88s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 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 : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 2 sgn 13 !; 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(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(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(p04d_1,axiom,
greatest_lower_bound(identity,a) = identity,
file('theBenchmark.p',p04d_1) ).
cnf(c_22,plain,
greatest_lower_bound(identity,a) = identity,
inference(clausify,[status(thm)],[p04d_1]) ).
fof(p04d_2,axiom,
greatest_lower_bound(identity,b) = identity,
file('theBenchmark.p',p04d_2) ).
cnf(c_23,plain,
greatest_lower_bound(identity,b) = identity,
inference(clausify,[status(thm)],[p04d_2]) ).
fof(prove_p04d,axiom,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('theBenchmark.p',prove_p04d) ).
cnf(c_24,plain,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
inference(clausify,[status(thm)],[prove_p04d]) ).
cnf(c_36,plain,
least_upper_bound(A,greatest_lower_bound(B,A)) = A,
inference(paramod,[status(thm)],[c_4,c_12]) ).
cnf(c_231,plain,
greatest_lower_bound(multiply(identity,A),multiply(a,A)) = multiply(identity,A),
inference(paramod,[status(thm)],[c_22,c_21]) ).
cnf(c_232,plain,
greatest_lower_bound(A,multiply(a,A)) = multiply(identity,A),
inference(paramod,[status(thm)],[c_1,c_231]) ).
cnf(c_66,plain,
greatest_lower_bound(A,multiply(a,A)) = A,
inference(paramod,[status(thm)],[c_1,c_232]) ).
cnf(c_233,plain,
greatest_lower_bound(identity,A) = greatest_lower_bound(identity,greatest_lower_bound(b,A)),
inference(paramod,[status(thm)],[c_23,c_7]) ).
cnf(c_67,plain,
greatest_lower_bound(identity,greatest_lower_bound(b,A)) = greatest_lower_bound(identity,A),
inference(copy,[status(thm)],[c_233]) ).
cnf(c_234,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_66,c_67]) ).
cnf(c_235,plain,
identity = greatest_lower_bound(identity,multiply(a,b)),
inference(paramod,[status(thm)],[c_23,c_234]) ).
cnf(c_213,plain,
greatest_lower_bound(identity,multiply(a,b)) = identity,
inference(copy,[status(thm)],[c_235]) ).
cnf(c_236,plain,
least_upper_bound(multiply(a,b),identity) = multiply(a,b),
inference(paramod,[status(thm)],[c_213,c_36]) ).
cnf(c_229,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(a,b),
inference(paramod,[status(thm)],[c_5,c_236]) ).
cnf(c_230,plain,
$false,
inference(resolve,[status(thm)],[c_229,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP172-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.84 % Computer : n001.cluster.edu
% 0.13/0.84 % Model : x86_64 x86_64
% 0.13/0.84 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.84 % Memory : 8046.5625MB
% 0.13/0.84 % OS : Linux 6.8.0-71-generic
% 0.13/0.84 % CPULimit : 300
% 0.13/0.84 % WCLimit : 300
% 0.13/0.84 % DateTime : Fri Sep 25 14:39:27 UTC 2026
% 0.13/0.84 % CPUTime :
% 0.13/0.84 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.84 % Process 3543284 was started by sandbox2 on n001,
% 0.13/0.84 % Fri Sep 25 14:39:27 2026
% 0.13/0.84 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.85
% 0.13/0.85 % From the command line: assign(max_seconds, 300).
% 0.13/0.88
% 0.13/0.88 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.88
% 0.13/0.88 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.13/0.88 % Length of proof is 17.
% 0.13/0.88 % Level of proof is 5.
% 0.13/0.88 % Maximum clause weight is 13.000.
% 0.13/0.88 % Given clauses 48.
% 0.13/0.88
% 0.13/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------